Euler characteristic of analogues of a Deligne-Lusztig variety for GL_n

2016/06/12 by Dongkwan Kim, Kim, Dongkwan
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1606.03759

arxiv created 2016/06/12 · arxiv updated 2016/06/14

Abstract

In this paper we give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne-Lusztig variety if we replace Frobenius morphism with conjugation by an element for GL_n. The main theorem states that it only depends on the unipotent part of the Jordan decomposition of an element and the conjugacy class in the Weyl group. Also it generalizes the formula of the Euler characteristic of a Springer fiber for type A.

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