Lie algebras and quantum groups via algebraic analysis

通过代数分析的李代数和量子群

• 批准号: 17340012
• 负责人: TANISAKI Toshiyuki
• 金额: $ 5.82万
• 依托单位: Osaka City University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17340012/
• 关键词: Lie algebras; Quantum groups; Algebraic analysis

1. Tanisaki investigated the action of the braid groups on the zero-weight spaces of the integral modules over quantized enveloping algebras. Under a certain condition on the representation the braid group action descends to the Hecke algebra, and a module over the Hecke algebra is obtained. In the case of type A all irreducible modules over the Hecke algebra is derived. Using the Kazhdan-Lusztig bases for the Hecke algebra modules and the global bases for the modules over the quantized enveloping algebras we can show that the construction above makes sense over rings. Hence it is possible to investigate modular representations by this method. Tanisaki gave a new proof of the conjecture by Lascoux-Leclerc-Thibon.2. Tanisaki investigated applications of the geometric Langlands correspondence to representation theory. Especially, he tried to obtain the twining character formula due to Naito etc. using geometric Langalands correspondence.3. Kashiwra investigated level zero fundamental modules over affine quantum algebras and Demazure modules.4. Shoji investigated representations of modified Ariki-Koike algebras introduced by himself. He also obtained interesting results on the corresponding q-Shur algebras.5. Naito investigated crystal bases of the extremal weight modules. Especially, he considered about the action of the diagram automorphisms and obtained results about the elements of the crystal base fixed by this group.6. Satio investigated Macdonald polynomials using Cherednik algebras.7. Kashiwara investigated representations of affine Hecke algebras of type B.8. Shoji investigated generalized Green functions and obtained results about some constant.

1. Tanisaki研究了辫子群在量子化包络代数上积分模的零权空间上的作用。在一定的表示条件下，辫子群作用下降到Hecke代数，得到了Hecke代数上的模。在类型A的情况下，导出了Hecke代数上的所有不可约模。利用Hecke代数模的Kazhdan-Lusztig基和量子化包络代数上的模的整体基，我们可以证明上面的构造在环上是有意义的。因此，它是可能的研究模表示的这种方法。谷崎对Lascoux-Leclerc-Thibon猜想给出了新的证明。谷崎研究应用几何朗兰兹对应表示论。特别是，他试图利用几何Langalands对应，得到内藤等人提出的缠绕特征公式. Kashiwara研究了仿射量子代数上的零级基本模和Demazure模.庄二调查表示修改有木小池代数介绍了自己。他还获得了有趣的结果，相应的q-舒尔代数。5。内藤研究了极值权模的晶体基。特别地，他考虑了图自同构的作用，得到了关于此群固定的晶基元素的结果. Satio研究麦克唐纳多项式使用Cherednik代数。7. Kashiwara研究了B.8型仿射Hecke代数的表示。Shoji研究了广义绿色函数，得到了一些关于常数的结果.

项目成果

Categories and Sheaves

• DOI: 10.1007/3-540-27950-4
• 发表时间: 2005-10
• 作者: 柏原 正樹;P. Schapira

The Beilinson-Bernstein correspondence for quantized enveloping Algebras

量化包络代数的 Beilinson-Bernstein 对应关系

• 发表时间: 2005
• 期刊: Mathematische Zeitschrift 250
• 作者: Kojima;Mizushima;Toshiyuki Tanisaki
• 通讯作者: Toshiyuki Tanisaki

Level zero fundamental representations over quantized affine algebras and Demazure modules

量化仿射代数和 Demazure 模块的零级基本表示

• 发表时间: 2005
• 期刊: Publ. Res. Inst. Math. Sci. 41
• 作者: A.Ichino;T.Ikeda;A. Ichino;T. Ikeda;平賀郁;K. Hiraga;K. Hiraga;池田保;A. Ichino;市野篤史;市野篤史;T. Ikeda;平賀郁;T. Ikeda;平賀郁;市野篤史;T.Shoji;D.Nakano;T.Tanisaki;T.Shoji;D.Nakano;N.Enomoto;S.Ariki;T.Tanisaki;M.Kashiwara
• 通讯作者: M.Kashiwara

Hecke Algebras of Classical Type and Their Representation Type

• DOI: 10.1112/s0024611505015236
• 发表时间: 2003-02
• 期刊: Proceedings of the London Mathematical Society
• 影响因子: 1.8
• 作者: S. Ariki

Proof of the modular branching rule for cyclotomic Hecke algebras

• DOI: 10.1016/j.jalgebra.2006.04.033
• 发表时间: 2005-11
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: S. Ariki