Quiver varieties and quantum affine algebras
箭袋簇和量子仿射代数
基本信息
- 批准号:13640019
- 负责人:
- 金额:$ 1.54万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2001
- 资助国家:日本
- 起止时间:2001 至 2002
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Standard modules, introduced by the head investigator via equivariant K-groups of quiver varieties, are proved to be isomorphic to extremal weight modules, introduced by Kashiwara. It was shown by Kashiwara that extremal weight modules have crystal bases. The head investigator proved that they are 'almost orthonormal' with respect to the natural inner product. This result is generalized to arbitrary afiine Lie algebras by a joint work with J. Beck. As an application, we prove the conjecture of Lusztig on cells of quantum affine algebras.On the other hand, the head investigator further studies t-analogs of q-characters. In particular, he gives 1) expressions in terms of Young tableaux for type A and D, and 2) generalization to the case when q is a root of unity. He also proved that the q-characters of a certain class of representations, called Kirillov-Reshetkhin modules, satisfy the recursive system called T-system.Also, the head investigator writes a C program for computing q-characters of finite dimensional representations of quantum affine algebras. He succeeded the calculation except Eg case. For Eg case, he can succeed if he has enough memory (some ten giga bytes) and computer time (about one week). But he did not have enough budget to perform the computation.The head investigator also studies operators on cohomology groups of moduli spaces of vector bundles over K3 surfaces, given by exceptional vector bundles.
证明了由首席研究员通过等变k群引入的标准模与由Kashiwara引入的极值权模同构。Kashiwara证明了极值重量模具有晶体基。首席研究员证明了它们对于自然内积是“几乎正交的”。通过与J. Beck的联合工作,将这一结果推广到任意正则李代数。作为一个应用,我们证明了Lusztig关于量子仿射代数细胞的猜想。另一方面,首席调查员进一步研究了q字符的t类似物。特别地,他给出了1)A和D类型的Young表的表达式,以及2)当q是单位的根时的推广。他还证明了一类称为Kirillov-Reshetkhin模的表示的q-字符满足称为t系统的递归系统。此外,首席研究员编写了一个C程序,用于计算量子仿射代数的有限维表示的q字符。除例外,他计算成功了。例如,如果他有足够的内存(大约10千兆字节)和计算机时间(大约一周),他就可以成功。但是他没有足够的预算来进行计算。首席研究者还研究了K3曲面上向量束模空间上同调群上的算子,这些算子由例外向量束给出。
项目成果
期刊论文数量(17)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Hiraku Nakajima: "t-analogs of q-characters of quantum affine of type An. Dn"Cont. Math.. (to appear).
Hiraku Nakajima:“An.Dn 类型量子仿射的 q 字符的 t 类似物”续。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Hiraku Nakajima: "Extremal weight modules of quantum affine algebras"Advanced Studies in Pure Mathematics, Representation Theory of Algebraic Groups. (to appear).
Hiraku Nakajima:《量子仿射代数的极值权模》纯数学高级研究,代数群表示论。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Hiraku Nakajima: "t-analogs of q-characters of quantum affine algebras of type A_n, D_n"Cont.Math.. (to appear).
Hiraku Nakajima:“A_n、D_n 型量子仿射代数的 q 字符的 t 类似物”Cont.Math..(即将出现)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Hiraku Nakajima: "Geometric constructions of representations of affine algebras"Proc. of Int. Congr. of Math.. vol. 1. 423-438 (2003)
Hiraku Nakajima:“仿射代数表示的几何构造”Proc。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Hiraku Nakajima: "Cells in quautum affine algebras"Proc. of Int. Conf. on Algebras Suzhou. (to appear).
Hiraku Nakajima:“量子仿射代数中的细胞”Proc。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
NAKAJIMA Hiraku其他文献
NAKAJIMA Hiraku的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('NAKAJIMA Hiraku', 18)}}的其他基金
Geometry of quiver varieties and representation theory
箭袋品种的几何和表示理论
- 批准号:
19340006 - 财政年份:2007
- 资助金额:
$ 1.54万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Quiver varieties, moduli spaces and representation theory
箭袋簇、模空间和表示理论
- 批准号:
17340005 - 财政年份:2005
- 资助金额:
$ 1.54万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Finite dimensional representations of quantum affine algebras
量子仿射代数的有限维表示
- 批准号:
15540023 - 财政年份:2003
- 资助金额:
$ 1.54万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Research on the classical limits of finite-dimensional representations over a quantum affine algebra
量子仿射代数有限维表示的经典极限研究
- 批准号:
16K17563 - 财政年份:2016
- 资助金额:
$ 1.54万 - 项目类别:
Grant-in-Aid for Young Scientists (B)
EAPSI: Quantum affine algebra representations and Box-Ball systems
EAPSI:量子仿射代数表示和 Box-Ball 系统
- 批准号:
1107105 - 财政年份:2011
- 资助金额:
$ 1.54万 - 项目类别:
Fellowship Award
Study on the path models for extremal weight modules over a quantum affine algebra
量子仿射代数极值权模路径模型研究
- 批准号:
14540006 - 财政年份:2002
- 资助金额:
$ 1.54万 - 项目类别:
Grant-in-Aid for Scientific Research (C)














{{item.name}}会员




