EXOTIC SYMMETRIC SPACES OF HIGHER LEVEL: SPRINGER CORRESPONDENCE FOR COMPLEX REFLECTION GROUPS
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- 作者：TOSHIAKI SHOJI
- 刊名：Transformation Groups
- 出版年：2016
- 出版时间：March 2016
- 年：2016
- 卷：21
- 期：1
- 页码：197-264
- 全文大小：822 KB
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[T]R. Travkin, Mirabolic Robinson–Schensted correspondence, Selecta Math. 14 (2009), 727–758. - 作者单位：TOSHIAKI SHOJI (1)
1. Department of Mathematics, Tongji University, 1239 Siping Road, Shanghai, 200092, People’s Republic of China - 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics
Topological Groups and Lie Groups
Algebra - 出版者：Birkh盲user Boston
- ISSN：1531-586X
文摘
Let G = GL(V) for a 2n-dimensional vector space V, and θ an involutive automorphism of G such that H = G θ ≃ Sp(V). Let be the set of unipotent elements g ∈ G such that θ(g) = g −1. For any integer r ≥ 2, we consider the variety , on which H acts diagonally. Let be a complex reflection group. In this paper, generalizing the known result for r = 2, we show that there exists a natural bijective correspondence (Springer correspondence) between the set of irreducible representations of W n,r and a certain set of H-equivariant simple perverse sheaves on . We also consider a similar problem for , on which G acts diagonally, where G = GL(V) for a finite-dimensional vector space V.