On total Springer representations for classical types
We give explicit formulas on total Springer representations for classical types. We also describe the characters of restrictions of such representations to a maximal parabolic subgroup isomorphic to a symmetric group. As a result, we give closed formulas for the Euler characteristic of Springer fibers.
KeywordsSpringer fiber Springer representation Weyl group Green polynomial Kostka-Foulkes polynomial
Mathematics Subject Classification20C99
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The author wishes to thank George Lusztig for having stimulating discussions with him and checking the draft of this paper. He is grateful to Jim Humphreys for his detailed remarks which help improve the readability of this paper. Also he thanks Gus Lonergan, Toshiaki Shoji, and an anonymous referee for useful comments.
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