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Soergel Calculus and Schubert Calculus Soergel微积分和Schubert微积分
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2015-02-17 DOI: 10.21915/BIMAS.2018303
Xuhua He, G. Williamson
{"title":"Soergel Calculus and Schubert Calculus","authors":"Xuhua He, G. Williamson","doi":"10.21915/BIMAS.2018303","DOIUrl":"https://doi.org/10.21915/BIMAS.2018303","url":null,"abstract":"We reduce some key calculations of compositions of morphisms between Soergel bimodules (\"Soergel calculus\") to calculations in the nil Hecke ring (\"Schubert calculus\"). This formula has several applications in modular representation theory.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"52 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2015-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88520327","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: 10
Positivity VS Negativity of Canonical Bases 标准碱基的正性与负性
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2015-01-04 DOI: 10.21915/BIMAS.2018201
Yiqiang Li, Weiqiang Wang
{"title":"Positivity VS Negativity of Canonical Bases","authors":"Yiqiang Li, Weiqiang Wang","doi":"10.21915/BIMAS.2018201","DOIUrl":"https://doi.org/10.21915/BIMAS.2018201","url":null,"abstract":"We provide examples for negativity of structure constants of the stably canonical basis of modified quantum $mathfrak{gl}_n$ and an analogous basis of modified quantum coideal algebra of $mathfrak{gl}_n$. In contrast, we construct the canonical basis of the modified quantum coideal algebra of $mathfrak{sl}_n$, establish the positivity of its structure constants, the positivity with respect to a geometric bilinear form as well as the positivity of its action on the tensor powers of the natural representation. The matrix coefficients of the transfer map on these Schur algebras with respect to the canonical bases are shown to be positive. Formulas for canonical basis of the iSchur algebra of rank one are obtained.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"38 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2015-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80604050","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: 31
A note on supersingular abelian varieties 关于超奇异阿贝尔变种的注释
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2014-12-22 DOI: 10.21915/bimas.2020102
Chia-Fu Yu
{"title":"A note on supersingular abelian varieties","authors":"Chia-Fu Yu","doi":"10.21915/bimas.2020102","DOIUrl":"https://doi.org/10.21915/bimas.2020102","url":null,"abstract":"In this note we show that any supersingular abelian variety is isogenous to a superspecial abelian variety without increasing field extensions. The proof uses minimal isogenies and the Galois descent. We then construct a superspecial abelian variety which not directly defined over a finite field. This answers negatively to a question of the author [J. Pure Appl. Alg., 2013] concerning of endomorphism algebras occurring in Shimura curves. Endomorphism algebras of supersingular elliptic curves over an arbitrary field are also investigated. We correct a main result of the author's paper [Math. Res. Let., 2010].","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"58 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2014-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80025072","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: 5
Finite groups of symplectic automorphisms of hyperkahler manifolds of type K3 K3型超kahler流形的辛自同构有限群
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2014-09-21 DOI: 10.21915/bimas.2019204
G. Hohn, G. Mason
{"title":"Finite groups of symplectic automorphisms of hyperkahler manifolds of type K3","authors":"G. Hohn, G. Mason","doi":"10.21915/bimas.2019204","DOIUrl":"https://doi.org/10.21915/bimas.2019204","url":null,"abstract":"We determine the possible finite groups $G$ of symplectic automorphisms of hyperkahler manifolds which are deformation equivalent to the second Hilbert scheme of a K3 surface. We prove that $G$ has such an action if, and only if, it is isomorphic to a subgroup of either the Mathieu group $M_{23}$ having at least four orbits in its natural permutation representation on $24$ elements, or one of two groups $3^{1+4}{:}2.2^2$ and $3^4{:}A_6$ associated to $mathcal{S}$-lattices in the Leech lattice. We describe in detail those $G$ which are maximal with respect to these properties, and (in most cases) we determine all deformation equivalence classes of such group actions. We also compare our results with the predictions of Mathieu Moonshine.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"86 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2014-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83059157","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: 18
Generic Property and Conjugacy Classes of Homogeneous Borel Subalgebras of Restricted Lie Algebras of Cartan Type (I): Type W Cartan型限制李代数的齐次Borel子代数的一般性质和共轭类(I): W型
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2014-04-04 DOI: 10.21915/bimas.2019302
B. Shu
{"title":"Generic Property and Conjugacy Classes of Homogeneous Borel Subalgebras of Restricted Lie Algebras of Cartan Type (I): Type W","authors":"B. Shu","doi":"10.21915/bimas.2019302","DOIUrl":"https://doi.org/10.21915/bimas.2019302","url":null,"abstract":"Let $(mathfrak{g},[p])$ be a finite-dimensional restricted Lie algebra over an algebraically closed field $mathbb{K}$ of characteristic $p>0$, and $G$ be the adjoint group of $mathfrak{g}$. We say that $mathfrak{g}$ satisfying the {sl generic property} if $mathfrak{g}$ admits generic tori introduced in cite{BFS}. A Borel subalgebra (or Borel for short) of $mathfrak{g}$ is by definition a maximal solvable subalgebra containing a maximal torus of $mathfrak{g}$, which is further called generic if additionally containing a generic torus. In this paper, we first settle a conjecture proposed by Premet in cite{Pr2} on regular Cartan subalgebras of restricted Lie algebras. We prove that the statement in the conjecture for a given $mathfrak{g}$ is valid if and only if it is the case when $mathfrak{g}$ satisfies the generic property. We then classify the conjugay classes of homogeneous Borel subalgebras of the restricted simple Lie algebras $mathfrak{g}=W(n)$ under $G$-conjugation when $p>3$, and present the representatives of these classes. Here $W(n)$ is the so-called Jacobson-Witt algebra, by definition the derivation algebra of the truncated polynomial ring $mathbb{K}[T_1,cdots,T_n]slash (T_1^p,cdots,T_n^p)$. We also describe the closed connected solvable subgroups of $G$ associated with those representative Borel subalgebras.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"23 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2014-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90077420","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
On Fusion Procedure For The Two-Parameter Quantum Algebra In Type A A型双参数量子代数的融合过程
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2014-02-15 DOI: 10.21915/BIMAS.2019102
N. Jing, Ming Liu
{"title":"On Fusion Procedure For The Two-Parameter Quantum Algebra In Type A","authors":"N. Jing, Ming Liu","doi":"10.21915/BIMAS.2019102","DOIUrl":"https://doi.org/10.21915/BIMAS.2019102","url":null,"abstract":"Finite dimensional irreducible modules of the two-parameter quantum enveloping algebra $U_{r,s}(mathfrak{sl}_n)$ are explicitly constructed using the fusion procedure when $rs^{-1}$ is generic. This provides an alternative and combinatorial description of the Schur-Weyl duality for the two-parameter quantum linear algebras of type $A$.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"285 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2014-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74959978","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
A Comparison of Landau-Ginzburg Models for Odd Dimensional Quadrics 奇维二次曲面的Landau-Ginzburg模型比较
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2013-06-17 DOI: 10.21915/BIMAS.2018301
C. Pech, K. Rietsch
{"title":"A Comparison of Landau-Ginzburg Models for Odd Dimensional Quadrics","authors":"C. Pech, K. Rietsch","doi":"10.21915/BIMAS.2018301","DOIUrl":"https://doi.org/10.21915/BIMAS.2018301","url":null,"abstract":"In [Rie08], the second author dened a Landau-Ginzburg model for homogeneous spaces G=P , as a regular function on an ane subvariety of the Langlands dual group. In this paper, we reformulate this LG model in the case of the odd-dimensional quadric Q2m 1 as a regular function Wt on the complement X of a particular anticanonical divisor in the projective space P 2m = P(H (Q2m 1;C) ). In fact, we express Wt in","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"41 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2013-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89219482","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
Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group 仿射Weyl群中的典型左细胞和最低双面细胞
IF 0.2
Bulletin of the Institute of Mathematics Academia Sinica New Series Pub Date : 2011-06-18 DOI: 10.21915/bimas.2018304
N. Xi
{"title":"Canonical Left Cells and the Lowest Two-sided Cell in an Affine Weyl Group","authors":"N. Xi","doi":"10.21915/bimas.2018304","DOIUrl":"https://doi.org/10.21915/bimas.2018304","url":null,"abstract":"We give some discussions to the relations between canonical left cells and the lowest two-sided cell of an affine Weyl group. In particular, we use the relations to construct irreducible modules attached to the lowest two-sided cell and some one dimensional representations of an affine Hecke algebra.","PeriodicalId":43960,"journal":{"name":"Bulletin of the Institute of Mathematics Academia Sinica New Series","volume":"1 1","pages":""},"PeriodicalIF":0.2,"publicationDate":"2011-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89569598","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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