Abstract
Let $G = GL_N(\mathbf{k})$, where $\mathbf{k}$ is an algebraically closed field of $\operatorname{ch} \mathbf{k} \ne 2$, and $\theta$ an involutive automorphism of $G$ such that $H = (G^{\theta})^0$ is isomorphic to $SO_N(\mathbf{k})$. Then $G^{\iota\theta} = \{ g \in G \mid \theta(g) = g^{-1}\}$ is regarded as a symmetric space $G/G^{\theta}$. Let $G^{\iota\theta}_{\operatorname{uni}}$ be the set of unipotent elements in $G^{\iota\theta}$. $H$ acts on $G^{\iota\theta}_{\operatorname{uni}}$ 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 $G^{\iota\theta}_{\operatorname{uni}}$ and irreducible representations of various symmetric groups.
Citation
Toshiaki SHOJI. Gao YANG. "Generalized Springer Correspondence for Symmetric Spaces Associated to Orthogonal Groups." Tokyo J. Math. 43 (2) 305 - 382, December 2020. https://doi.org/10.3836/tjm/1502179318
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