Generalized Springer Correspondence for Symmetric Spaces Associated to Orthogonal Groups
Generalized Springer Correspondence for Symmetric Spaces Associated to Orthogonal Groups
复制标题
与正交群相关的对称空间的广义施普林格对应
DOI：
10.3836/tjm/1502179318
复制
发表时间：
2017-08
影响因子：
0.6
通讯作者：
Yang Gao
中科院分区：
文献类型：
--
作者：
Shoji Toshiaki;Yang Gao
Let $G = GL_N$ over an algebraically closed field of odd characteristic, and $\theta$ an involutive automorphism on $G$ such that $H = (G^{\theta})^0$ is isomorphic to $SO_N$. Then $G^{\iota\theta} = \{ g \in G \mid \theta(g) = g^{-1} \}$ is regarded as a symmetric space $G/G^{\theta}$. Let $G^{\iota\theta}_{uni}$ be the set of unipotent elements in $G^{\iota\theta}$. $H$ acts on $G^{\iota\theta}_{uni}$ by the conjugation. As an analogue of the generalized Springer correspondence in the case of reductive groups, we establish in this paper the generalized Springer correspondence between $H$-orbits in $G^{\iota\theta}_{uni}$ and irreducible representations of various symmetric groups.
Let $G = GL_N$ over an algebraically closed field of odd characteristic, and $\theta$ an involutive automorphism on $G$ such that $H = (G^{\theta})^0$ is isomorphic to $SO_N$. Then $G^{\iota\theta} = \{ g \in G \mid \theta(g) = g^{-1} \}$ is regarded as a symmetric space $G/G^{\theta}$. Let $G^{\iota\theta}_{uni}$ be the set of unipotent elements in $G^{\iota\theta}$. $H$ acts on $G^{\iota\theta}_{uni}$ by the conjugation. As an analogue of the generalized Springer correspondence in the case of reductive groups, we establish in this paper the generalized Springer correspondence between $H$-orbits in $G^{\iota\theta}_{uni}$ and irreducible representations of various symmetric groups.
登录
查看更多内容
影响因子：
1.8
作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
通讯作者：
Tsao-Hsien Chen;K. Vilonen;Ting Xue
DOI：
10.1090/s0273-0979-1981-14902-8
发表时间：
1981-03
影响因子：
1.3
作者：
R. Stanley
通讯作者：
R. Stanley
DOI：
10.1090/ert/500
发表时间：
2016-02
期刊：
arXiv: Representation Theory
影响因子：
--
作者：
G. Lusztig;Zhiwei Yun
通讯作者：
G. Lusztig;Zhiwei Yun
影响因子：
1.7
作者：
G. Lusztig
通讯作者：
G. Lusztig
影响因子：
0.7
作者：
T. Shoji;K. Sorlin
通讯作者：
T. Shoji;K. Sorlin