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On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case

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Abstract

Let W be the Weyl group of type BCn. We first provide restriction formulas of the total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case to the maximal parabolic subgroup of W which is of type BCn− 1. Then we show that these two restriction formulas are equivalent, and discuss how the results can be used to examine the existence of affine pavings of Springer fibers corresponding to the symplectic Lie algebra in characteristic 2.

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Acknowledgements

The author is grateful to George Lusztig for helpful comments on this topic.

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Authors and Affiliations

  1. School of Mathematics, University of Minnesota Twin Cities, Minneapolis, MN, 55455, U.S.A.

    Dongkwan Kim

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  1. Dongkwan Kim
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Correspondence to Dongkwan Kim.

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Presented by: Pramod Achar

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Kim, D. On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case. Algebr Represent Theor 26, 679–715 (2023). https://doi.org/10.1007/s10468-021-10109-y

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