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High-dimensional ellipsoids converge to Gaussian spaces 高维椭球体收敛于高斯空间
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-10-17 DOI: 10.2969/jmsj/86648664
Daisuke Kazukawa, Takashi Shioya
{"title":"High-dimensional ellipsoids converge to Gaussian spaces","authors":"Daisuke Kazukawa, Takashi Shioya","doi":"10.2969/jmsj/86648664","DOIUrl":"https://doi.org/10.2969/jmsj/86648664","url":null,"abstract":"We prove the convergence of (solid) ellipsoids to a Gaussian space in Gromov's concentration/weak topology as the dimension diverges to infinity. This gives the first discovered example of an irreducible nontrivial convergent sequence in the concentration topology, where ‘irreducible nontrivial’ roughly means to be not constructed from Lévy families nor box convergent sequences.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 5
Parabolic BGG categories and their block decomposition for Lie superalgebras of Cartan type Cartan型Lie超代数的抛物型BGG范畴及其块分解
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-10-11 DOI: 10.2969/jmsj/90439043
Fei-Fei DUAN, Bin SHU, Yu-Feng YAO
{"title":"Parabolic BGG categories and their block decomposition for Lie superalgebras of Cartan type","authors":"Fei-Fei DUAN, Bin SHU, Yu-Feng YAO","doi":"10.2969/jmsj/90439043","DOIUrl":"https://doi.org/10.2969/jmsj/90439043","url":null,"abstract":"In this paper, we study the parabolic BGG categories for graded Lie superalgebras of Cartan type over the field of complex numbers. The gradation of such a Lie superalgebra $mathfrak{g}$ naturally arises, with the zero component $mathfrak{g}_{0}$ being a reductive Lie algebra. We first show that there are only two proper parabolic subalgebras containing Levi subalgebra $mathfrak{g}_{0}$: the “maximal one” $mathsf{P}_{max}$ and the “minimal one” $mathsf{P}_{min}$. Furthermore, the parabolic BGG category arising from $mathsf{P}_{max}$ essentially turns out to be a subcategory of the one arising from $mathsf{P}_{min}$. Such a priority of $mathsf{P}_{min}$ in the sense of representation theory reduces the question to the study of the “minimal parabolic” BGG category $mathcal{O}^{min}$ associated with $mathsf{P}_{min}$. We prove the existence of projective covers of simple objects in these categories, which enables us to establish a satisfactory block theory. Most notably, our main results are as follows. (1) We classify and obtain a precise description of the blocks of $mathcal{O}^{min}$. (2) We investigate indecomposable tilting and indecomposable projective modules in $mathcal{O}^{min}$, and compute their character formulas.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210218","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quenched invariance principle for a reflecting diffusion in a continuum percolation cluster 连续渗流团簇中反射扩散的淬灭不变性原理
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-10-03 DOI: 10.2969/jmsj/89198919
Yutaka TAKEUCHI
{"title":"Quenched invariance principle for a reflecting diffusion in a continuum percolation cluster","authors":"Yutaka TAKEUCHI","doi":"10.2969/jmsj/89198919","DOIUrl":"https://doi.org/10.2969/jmsj/89198919","url":null,"abstract":"We consider a continuum percolation built over stationary ergodic point processes. Assuming that the occupied region has a unique unbounded cluster and the cluster satisfies volume regularity and isoperimetric condition, we prove a quenched invariance principle for reflecting diffusions on the cluster.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135695911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Tableau formulas for skew Grothendieck polynomials 斜格罗滕迪克多项式的表格公式
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-09-27 DOI: 10.2969/jmsj/89928992
Harry TAMVAKIS
{"title":"Tableau formulas for skew Grothendieck polynomials","authors":"Harry TAMVAKIS","doi":"10.2969/jmsj/89928992","DOIUrl":"https://doi.org/10.2969/jmsj/89928992","url":null,"abstract":"An element of a Weyl group of classical type is skew if it is the left factor in a reduced factorization of a Grassmannian element. The skew Grothendieck polynomials are those which are indexed by skew elements of the Weyl group. We define set-valued tableaux which are fillings of the associated skew Young diagrams and use them to prove tableau formulas for the skew double Grothendieck polynomials in all four classical Lie types. We deduce tableau formulas for the Grassmannian Grothendieck polynomials and the $K$-theoretic analogues of the (double mixed) skew Stanley functions in the respective Lie types.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A refined transversality theorem on linear perturbations and its applications 线性摄动的一个改进的横截定理及其应用
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-09-15 DOI: 10.2969/jmsj/90559055
Shunsuke ICHIKI
{"title":"A refined transversality theorem on linear perturbations and its applications","authors":"Shunsuke ICHIKI","doi":"10.2969/jmsj/90559055","DOIUrl":"https://doi.org/10.2969/jmsj/90559055","url":null,"abstract":"In this paper, we establish a refined transversality theorem on linear perturbations from a new perspective of Hausdorff measures. Furthermore, we give its applications not only to singularity theory but also to multiobjective optimization.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135436906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized Bott–Cattaneo–Rossi invariants in terms of Alexander polynomials Alexander多项式的广义bot - cattaneo - rossi不变量
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-08-29 DOI: 10.2969/jmsj/88168816
David Leturcq
{"title":"Generalized Bott–Cattaneo–Rossi invariants in terms of Alexander polynomials","authors":"David Leturcq","doi":"10.2969/jmsj/88168816","DOIUrl":"https://doi.org/10.2969/jmsj/88168816","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44669527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Characterizations of pretzel knots which are simple-ribbon 椒盐卷饼结的特征是简单的缎带
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-06-14 DOI: 10.2969/jmsj/89438943
T. Shibuya, Tatsuya Tsukamoto, Y. Uchida, T. Ishikawa
{"title":"Characterizations of pretzel knots which are simple-ribbon","authors":"T. Shibuya, Tatsuya Tsukamoto, Y. Uchida, T. Ishikawa","doi":"10.2969/jmsj/89438943","DOIUrl":"https://doi.org/10.2969/jmsj/89438943","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45063042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
$k$-color region select game $k$-颜色区域选择游戏
4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-04-26 DOI: 10.2969/jmsj/89408940
Ahmet BATAL, Neslihan GÜGÜMCÜ
{"title":"$k$-color region select game","authors":"Ahmet BATAL, Neslihan GÜGÜMCÜ","doi":"10.2969/jmsj/89408940","DOIUrl":"https://doi.org/10.2969/jmsj/89408940","url":null,"abstract":"The region select game, introduced by Ayaka Shimizu, Akio Kawauchi and Kengo Kishimoto, is a game that is played on knot diagrams whose crossings are endowed with two colors. The game is based on the region crossing change moves that induce an unknotting operation on knot diagrams. We generalize the region select game to be played on a knot diagram endowed with $k$-colors at its vertices for $2 leq k leq infty$.","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136380014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Fourier coefficients of Siegel Eisenstein series of degree 3 of an odd prime level with the quadratic character 二次奇素数阶3次Siegel Eisenstein级数的傅里叶系数
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-04-26 DOI: 10.2969/jmsj/88988898
Keiichi Gunji
{"title":"On the Fourier coefficients of Siegel Eisenstein series of degree 3 of an odd prime level with the quadratic character","authors":"Keiichi Gunji","doi":"10.2969/jmsj/88988898","DOIUrl":"https://doi.org/10.2969/jmsj/88988898","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41761840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A topological product decomposition of Busemann space Busemann空间的拓扑乘积分解
IF 0.7 4区 数学
Journal of the Mathematical Society of Japan Pub Date : 2023-04-24 DOI: 10.2969/jmsj/89738973
Tomohiro Fukaya
{"title":"A topological product decomposition of Busemann space","authors":"Tomohiro Fukaya","doi":"10.2969/jmsj/89738973","DOIUrl":"https://doi.org/10.2969/jmsj/89738973","url":null,"abstract":"","PeriodicalId":49988,"journal":{"name":"Journal of the Mathematical Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42672394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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