Let for an -dimensional vector space over an algebraically closed field , and the fixed point subgroup of under an involution on . In the case where , the generalized Springer correspondence for the unipotent variety of the symmetric space was described in [SY], assuming that . The definition of given there, and of the symmetric space arising from , make sense even if . In this paper, we discuss the Springer correspondence for those symmetric spaces with even characteristic. We show, if is even, that the Springer correspondence is reduced to that of symplectic Lie algebras in , which was determined by Xue. While if is odd, the number of -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 .
"Symmetric Spaces Associated to Classical Groups with Even Characteristic." Tokyo J. Math. 45 (1) 1 - 67, June 2022. https://doi.org/10.3836/tjm/1502179368