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Whitney stratifications are conically smooth 惠特尼分层呈圆锥形光滑
2区 数学
Selecta Mathematica-New Series Pub Date : 2023-09-15 DOI: 10.1007/s00029-023-00877-4
Guglielmo Nocera, Marco Volpe
{"title":"Whitney stratifications are conically smooth","authors":"Guglielmo Nocera, Marco Volpe","doi":"10.1007/s00029-023-00877-4","DOIUrl":"https://doi.org/10.1007/s00029-023-00877-4","url":null,"abstract":"Abstract The notion of conically smooth structure on a stratified space was introduced by Ayala, Francis and Tanaka. This is a very well behaved analogue of a differential structure in the context of stratified topological spaces, satisfying good properties such as the existence of resolutions of singularities and handlebody decompositions. In this paper we prove Ayala, Francis and Tanaka’s conjecture that any Whitney stratified space admits a canonical conically smooth structure. We thus establish a connection between the theory of conically smooth spaces and the classical examples of stratified spaces from differential topology.","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135353865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
On the affine Hecke category for SL3documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$SL_3$$end{document} On the affine Hecke category for SL3documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$SL_3$$end{document}
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-08-18 DOI: 10.1007/s00029-023-00864-9
Nicolas Libedinsky, L. Patimo
{"title":"On the affine Hecke category for SL3documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$SL_3$$end{document}","authors":"Nicolas Libedinsky, L. Patimo","doi":"10.1007/s00029-023-00864-9","DOIUrl":"https://doi.org/10.1007/s00029-023-00864-9","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"6 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79584209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The ν+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nu ^+$$end{document}-equivalence classes of genus one knots The ν+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nu ^+$$end{document}-equivalence classes of genus one knots
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-08-17 DOI: 10.1007/s00029-023-00867-6
Kouki Sato
{"title":"The ν+documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nu ^+$$end{document}-equivalence classes of genus one knots","authors":"Kouki Sato","doi":"10.1007/s00029-023-00867-6","DOIUrl":"https://doi.org/10.1007/s00029-023-00867-6","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"30 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87818652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bifurcation of a disappearance of a non-compact heteroclinic curve 非紧致异斜曲线消失的分岔
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-07-31 DOI: 10.1007/s00029-023-00863-w
O. Pochinka, Valeriya I. Shmukler, E. Talanova
{"title":"Bifurcation of a disappearance of a non-compact heteroclinic curve","authors":"O. Pochinka, Valeriya I. Shmukler, E. Talanova","doi":"10.1007/s00029-023-00863-w","DOIUrl":"https://doi.org/10.1007/s00029-023-00863-w","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"32 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80001791","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Moduli of relative stable maps to P1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {P}^1$$end{document}: cut Moduli of relative stable maps to P1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {P}^1$$end{document}: cut
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-07-14 DOI: 10.1007/s00029-023-00857-8
S. Kannan
{"title":"Moduli of relative stable maps to P1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$mathbb {P}^1$$end{document}: cut","authors":"S. Kannan","doi":"10.1007/s00029-023-00857-8","DOIUrl":"https://doi.org/10.1007/s00029-023-00857-8","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"9 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78474762","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Horn(p,q)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Horn}(p,q)$$end{document}
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-07-04 DOI: 10.1007/s00029-023-00855-w
P. Paradan
{"title":"Horn(p,q)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$textrm{Horn}(p,q)$$end{document}","authors":"P. Paradan","doi":"10.1007/s00029-023-00855-w","DOIUrl":"https://doi.org/10.1007/s00029-023-00855-w","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"83 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88624901","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On V-filtration, Hodge filtration and Fourier transform 关于v滤波,霍奇滤波和傅里叶变换
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-07-03 DOI: 10.1007/s00029-023-00850-1
Qianyu Chen, Bradley Dirks
{"title":"On V-filtration, Hodge filtration and Fourier transform","authors":"Qianyu Chen, Bradley Dirks","doi":"10.1007/s00029-023-00850-1","DOIUrl":"https://doi.org/10.1007/s00029-023-00850-1","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"95 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73069980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
On classical tensor categories attached to the irreducible representations of the general linear supergroups GL(n|n)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setle On classical tensor categories attached to the irreducible representations of the general linear supergroups GL(n|n)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setle
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-04-20 DOI: 10.1007/s00029-023-00842-1
T. Heidersdorf, R. Weissauer
{"title":"On classical tensor categories attached to the irreducible representations of the general linear supergroups GL(n|n)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setle","authors":"T. Heidersdorf, R. Weissauer","doi":"10.1007/s00029-023-00842-1","DOIUrl":"https://doi.org/10.1007/s00029-023-00842-1","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"34 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79767518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Analytic functions and Nash functions along curves 解析函数和沿曲线的纳什函数
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-01-16 DOI: 10.1007/s00029-022-00824-9
W. Kucharz, Krzysztof Kurdyka
{"title":"Analytic functions and Nash functions along curves","authors":"W. Kucharz, Krzysztof Kurdyka","doi":"10.1007/s00029-022-00824-9","DOIUrl":"https://doi.org/10.1007/s00029-022-00824-9","url":null,"abstract":"","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"16 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88206653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Equivariant multiplicities via representations of quantum affine algebras. 量子仿射代数表示的等变多重性。
IF 1.4 2区 数学
Selecta Mathematica-New Series Pub Date : 2023-01-01 Epub Date: 2022-11-17 DOI: 10.1007/s00029-022-00805-y
Elie Casbi, Jian-Rong Li
{"title":"Equivariant multiplicities via representations of quantum affine algebras.","authors":"Elie Casbi, Jian-Rong Li","doi":"10.1007/s00029-022-00805-y","DOIUrl":"https://doi.org/10.1007/s00029-022-00805-y","url":null,"abstract":"<p><p>For any simply-laced type simple Lie algebra <math><mi>g</mi></math> and any height function <math><mi>ξ</mi></math> adapted to an orientation <i>Q</i> of the Dynkin diagram of <math><mi>g</mi></math> , Hernandez-Leclerc introduced a certain category <math> <msup><mrow><mi>C</mi></mrow> <mrow><mo>≤</mo> <mi>ξ</mi></mrow> </msup> </math> of representations of the quantum affine algebra <math> <mrow><msub><mi>U</mi> <mi>q</mi></msub> <mrow><mo>(</mo> <mover><mi>g</mi> <mo>^</mo></mover> <mo>)</mo></mrow> </mrow> </math> , as well as a subcategory <math><msub><mi>C</mi> <mi>Q</mi></msub> </math> of <math> <msup><mrow><mi>C</mi></mrow> <mrow><mo>≤</mo> <mi>ξ</mi></mrow> </msup> </math> whose complexified Grothendieck ring is isomorphic to the coordinate ring <math><mrow><mi>C</mi> <mo>[</mo> <mi>N</mi> <mo>]</mo></mrow> </math> of a maximal unipotent subgroup. In this paper, we define an algebraic morphism <math> <msub><mover><mi>D</mi> <mo>~</mo></mover> <mi>ξ</mi></msub> </math> on a torus <math> <msup><mrow><mi>Y</mi></mrow> <mrow><mo>≤</mo> <mi>ξ</mi></mrow> </msup> </math> containing the image of <math> <mrow><msub><mi>K</mi> <mn>0</mn></msub> <mrow><mo>(</mo> <msup><mrow><mi>C</mi></mrow> <mrow><mo>≤</mo> <mi>ξ</mi></mrow> </msup> <mo>)</mo></mrow> </mrow> </math> under the truncated <i>q</i>-character morphism. We prove that the restriction of <math> <msub><mover><mi>D</mi> <mo>~</mo></mover> <mi>ξ</mi></msub> </math> to <math> <mrow><msub><mi>K</mi> <mn>0</mn></msub> <mrow><mo>(</mo> <msub><mi>C</mi> <mi>Q</mi></msub> <mo>)</mo></mrow> </mrow> </math> coincides with the morphism <math><mover><mi>D</mi> <mo>¯</mo></mover> </math> recently introduced by Baumann-Kamnitzer-Knutson in their study of equivariant multiplicities of Mirković-Vilonen cycles. This is achieved using the T-systems satisfied by the characters of Kirillov-Reshetikhin modules in <math><msub><mi>C</mi> <mi>Q</mi></msub> </math> , as well as certain results by Brundan-Kleshchev-McNamara on the representation theory of quiver Hecke algebras. This alternative description of <math><mover><mi>D</mi> <mo>¯</mo></mover> </math> allows us to prove a conjecture by the first author on the distinguished values of <math><mover><mi>D</mi> <mo>¯</mo></mover> </math> on the flag minors of <math><mrow><mi>C</mi> <mo>[</mo> <mi>N</mi> <mo>]</mo></mrow> </math> . We also provide applications of our results from the perspective of Kang-Kashiwara-Kim-Oh's generalized Schur-Weyl duality. Finally, we use Kashiwara-Kim-Oh-Park's recent constructions to define a cluster algebra <math> <msub><mover><mi>A</mi> <mo>¯</mo></mover> <mi>Q</mi></msub> </math> as a subquotient of <math> <mrow><msub><mi>K</mi> <mn>0</mn></msub> <mrow><mo>(</mo> <msup><mrow><mi>C</mi></mrow> <mrow><mo>≤</mo> <mi>ξ</mi></mrow> </msup> <mo>)</mo></mrow> </mrow> </math> naturally containing <math><mrow><mi>C</mi> <mo>[</mo> <mi>N</mi> <mo>]</mo></mrow> </math> , and suggest the existence of an analogue of the Mirković-Vilo","PeriodicalId":49551,"journal":{"name":"Selecta Mathematica-New Series","volume":"29 1","pages":"9"},"PeriodicalIF":1.4,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9707734/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35207479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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