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Symmetry breaking differential operators for tensor products of spinorial representations. 旋量表示张量积的对称破缺微分算子。
arXiv: Representation Theory Pub Date : 2020-12-17 DOI: 10.3842/SIGMA.2021.049
J. Clerc, K. Koufany
{"title":"Symmetry breaking differential operators for tensor products of spinorial representations.","authors":"J. Clerc, K. Koufany","doi":"10.3842/SIGMA.2021.049","DOIUrl":"https://doi.org/10.3842/SIGMA.2021.049","url":null,"abstract":"Let $mathbb S$ be a Clifford module for the complexified Clifford algebra $Cell(mathbb R^n)$, $mathbb S'$ its dual, $rho$ and $rho'$ be the corresponding representations of the spin group $Spin(mathbb R^n)$. The group $G=Spin(mathbb R^{1,n+1})$ is the (twofold covering) of the conformal group of $mathbb R^n$. For $lambda, muin mathbb C$, let $pi_{rho, lambda}$ (resp. $pi_{rho',mu}$) be the spinorial representation of $G$ on $ mathbb S$-valued $lambda$-densities (resp. $mathbb S'$-valued $mu$-densities) on $mathbb R^n$. For $0leq kleq n$ and $min mathbb N$, we construct a symmetry breaking differential operator $B_{k;lambda,mu}^{(m)}$ from $C^infty(mathbb R^n times mathbb R^n, mathbb Sotimes mathbb S')$ into $C^infty(mathbb R^n, Lambda^*_k(mathbb R^n))$ which intertwines the representations $pi_{rho, lambda}otimes pi_{rho',mu} $ and $pi_{tau^*_k,lambda+mu+2m}$, where $tau^*_k$ is the representation of $Spin(mathbb R^n)$ on $Lambda^*_k(mathbb R^n)$.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121049717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Irreducible components of two-row Springer fibers for all classical types 两排施普林格纤维的不可还原成分，适用于所有经典类型
arXiv: Representation Theory Pub Date : 2020-11-26 DOI: 10.1090/proc/15965
Mee Seong Im, C. Lai, A. Wilbert
{"title":"Irreducible components of two-row Springer fibers for all classical types","authors":"Mee Seong Im, C. Lai, A. Wilbert","doi":"10.1090/proc/15965","DOIUrl":"https://doi.org/10.1090/proc/15965","url":null,"abstract":"We give an explicit description of the irreducible components of two-row Springer fibers for all classical types using cup diagrams. Cup diagrams can be used to label the irreducible components of two-row Springer fibers. Given a cup diagram, we explicitly write down all flags contained in the component associated to the cup diagram. This generalizes results by Stroppel--Webster and Fung to all classical types.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131241158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
PRV for the fusion product, the case $$uplambda gg mu $$ 融合产物的PRV $$uplambda gg mu $$
arXiv: Representation Theory Pub Date : 2020-11-22 DOI: 10.1007/S00209-021-02754-2
A. Boysal
{"title":"PRV for the fusion product, the case $$uplambda gg mu $$","authors":"A. Boysal","doi":"10.1007/S00209-021-02754-2","DOIUrl":"https://doi.org/10.1007/S00209-021-02754-2","url":null,"abstract":"","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128365195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Norms and Cayley–Hamilton algebras 范数与Cayley-Hamilton代数
arXiv: Representation Theory Pub Date : 2020-11-08 DOI: 10.4171/rlm/925
C. Procesi
{"title":"Norms and Cayley–Hamilton algebras","authors":"C. Procesi","doi":"10.4171/rlm/925","DOIUrl":"https://doi.org/10.4171/rlm/925","url":null,"abstract":"We develop the general Theory of Cayley Hamilton algebras using norms and compare with the approach, valid only in characteristic 0, using traces and presented in a previous paper $T$-ideals of Cayley Hamilton algebras, 2020, arXiv:2008.02222","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"134 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116351066","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Locally finite representations over Noetherian Hopf algebras Noetherian Hopf代数上的局部有限表示
arXiv: Representation Theory Pub Date : 2020-10-27 DOI: 10.1090/proc/15747
Can Hat.ipouglu, C. Lomp
{"title":"Locally finite representations over Noetherian Hopf algebras","authors":"Can Hat.ipouglu, C. Lomp","doi":"10.1090/proc/15747","DOIUrl":"https://doi.org/10.1090/proc/15747","url":null,"abstract":"We study finite dimensional representations over some Noetherian algebras over a field of characteristic zero. More precisely, we give necessary and sufficient conditions for the category of locally finite dimensional representations to be closed under taking injective hulls and extend results known for group rings and enveloping algebras to Ore extensions, Hopf crossed products and affine Hopf algebras of low Gelfand-Kirillov dimension.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123286004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Higher ideal approximation theory 高理想近似理论
arXiv: Representation Theory Pub Date : 2020-10-25 DOI: 10.1090/tran/8562
J. Asadollahi, S. Sadeghi
{"title":"Higher ideal approximation theory","authors":"J. Asadollahi, S. Sadeghi","doi":"10.1090/tran/8562","DOIUrl":"https://doi.org/10.1090/tran/8562","url":null,"abstract":"Let ${mathscr{C}}$ be an $n$-cluster tilting subcategory of an exact category $({mathscr{A}}, {mathscr{E}})$, where $n geq 1$ is an integer. It is proved by Jasso that if $n> 1$, then ${mathscr{C}}$ although is no longer exact, but has a nice structure known as $n$-exact structure. In this new structure conflations are called admissible $n$-exact sequences and are ${mathscr{E}}$-acyclic complexes with $n+2$ terms in ${mathscr{C}}$. Since their introduction by Iyama, cluster tilting subcategories has gained a lot of traction, due largely to their links and applications to many research areas, many of them unexpected. On the other hand, ideal approximation theory, that is a gentle generalization of the classical approximation theory and deals with morphisms and ideals instead of objects and subcategories, is an active area that has been the subject of several researches. Our aim in this paper is to introduce the so-called `ideal approximation theory' into `higher homological algebra'. To this end, we introduce some important notions in approximation theory into the theory of $n$-exact categories and prove some results. In particular, the higher version of the notions such as ideal cotorsion pairs, phantom ideals, Salce's Lemma and Wakamatsu's Lemma for ideals will be introduced and studied. Our results motivate the definitions and show that $n$-exact categories are the appropriate context for the study of `higher ideal approximation theory'.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121754338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64 64阶初等阿贝尔缺陷群的主块的Morita等价类
arXiv: Representation Theory Pub Date : 2020-10-15 DOI: 10.21538/0134-4889-2021-27-1-220-239
C. G. Ardito
{"title":"Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64","authors":"C. G. Ardito","doi":"10.21538/0134-4889-2021-27-1-220-239","DOIUrl":"https://doi.org/10.21538/0134-4889-2021-27-1-220-239","url":null,"abstract":"We classify the Morita equivalence classes of principal blocks with elementary abelian defect groups of order 64 with respect to a complete discrete valuation ring with an algebraically closed residue field of characteristic two.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116577092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras 根平方零Nakayama代数的Auslander代数上的可倾模分类
arXiv: Representation Theory Pub Date : 2020-10-14 DOI: 10.1142/s0219498822500414
Xiaojin Zhang
{"title":"Classifying tilting modules over the Auslander algebras of radical square zero Nakayama algebras","authors":"Xiaojin Zhang","doi":"10.1142/s0219498822500414","DOIUrl":"https://doi.org/10.1142/s0219498822500414","url":null,"abstract":"Let $Lambda$ be a radical square zero Nakayama algebra with $n$ simple modules and let $Gamma$ be the Auslander algebra of $Lambda$. Then every indecomposable direct summand of a tilting $Gamma$-module is either simple or projective. Moreover, if $Lambda$ is self-injective, then the number of tilting $Gamma$-modules is $2^n$; otherwise, the number of tilting $Gamma$-modules is $2^{n-1}$.","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115335793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
All quasihereditary algebras with a regular exact Borel subalgebra 具有正则精确Borel子代数的所有拟遗传代数
arXiv: Representation Theory Pub Date : 2020-10-08 DOI: 10.1016/J.AIM.2021.107751
T. Conde
{"title":"All quasihereditary algebras with a regular exact Borel subalgebra","authors":"T. Conde","doi":"10.1016/J.AIM.2021.107751","DOIUrl":"https://doi.org/10.1016/J.AIM.2021.107751","url":null,"abstract":"","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"47 6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"118512312","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Spherical birational sheets in reductive groups 还原群中的球形双胞片
arXiv: Representation Theory Pub Date : 2020-08-31 DOI: 10.1016/j.jalgebra.2021.07.036.
F. Ambrosio, M. Costantini
{"title":"Spherical birational sheets in reductive groups","authors":"F. Ambrosio, M. Costantini","doi":"10.1016/j.jalgebra.2021.07.036.","DOIUrl":"https://doi.org/10.1016/j.jalgebra.2021.07.036.","url":null,"abstract":"","PeriodicalId":275006,"journal":{"name":"arXiv: Representation Theory","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131980306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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