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June 2022 Symmetric Spaces Associated to Classical Groups with Even Characteristic
Junbin Dong, Toshiaki Shoji, Gao Yang
Tokyo J. Math. 45(1): 1-67 (June 2022). DOI: 10.3836/tjm/1502179368


Let G=GL(V) for an N-dimensional vector space V over an algebraically closed field k, and Gθ the fixed point subgroup of G under an involution θ on G. In the case where Gθ=O(V), the generalized Springer correspondence for the unipotent variety of the symmetric space G/Gθ was described in [SY], assuming that ch k2. The definition of θ given there, and of the symmetric space arising from θ, make sense even if ch k=2. In this paper, we discuss the Springer correspondence for those symmetric spaces with even characteristic. We show, if N is even, that the Springer correspondence is reduced to that of symplectic Lie algebras in ch k=2, which was determined by Xue. While if N is odd, the number of Gθ-orbits in the unipotent variety is infinite, and a very similar phenomenon occurs as in the case of exotic symmetric space of higher level, namely of level r=3.


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Junbin Dong. Toshiaki Shoji. Gao Yang. "Symmetric Spaces Associated to Classical Groups with Even Characteristic." Tokyo J. Math. 45 (1) 1 - 67, June 2022.


Received: 24 January 2020; Revised: 15 October 2021; Published: June 2022
First available in Project Euclid: 12 August 2022

Digital Object Identifier: 10.3836/tjm/1502179368

Primary: 20G05

Keywords: even characteristic , Springer correspondence , Symmetric space

Rights: Copyright © 2022 Publication Committee for the Tokyo Journal of Mathematics


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Vol.45 • No. 1 • June 2022
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