Euler characteristic of analogues of a Deligne–Lusztig variety for GLn

Dongkwan Kim

doi:10.1016/j.jalgebra.2018.03.011

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

Dongkwan Kim

Research output: Contribution to journal › Article › peer-review

Abstract

We give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne–Lusztig variety, denoted Y_w,g, which is attached to an element w in the Weyl group of GL_n and g∈GL_n. The main theorem of this paper states that the Euler characteristic of Y_w,g only depends on the unipotent part of the Jordan decomposition of g and the conjugacy class of w. It generalizes the formula of the Euler characteristic of Springer fibers for type A.

Original language	English (US)
Pages (from-to)	321-338
Number of pages	18
Journal	Journal of Algebra
Volume	505
DOIs	https://doi.org/10.1016/j.jalgebra.2018.03.011
State	Published - Jul 1 2018
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2018 Elsevier Inc.

Keywords

Deligne–Lusztig character
Deligne–Lusztig variety
Euler characteristic
Springer fiber

Publisher link

10.1016/j.jalgebra.2018.03.011

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AB - We give a combinatorial formula to calculate the Euler characteristic of an analogue of a Deligne–Lusztig variety, denoted Yw,g, which is attached to an element w in the Weyl group of GLn and g∈GLn. The main theorem of this paper states that the Euler characteristic of Yw,g only depends on the unipotent part of the Jordan decomposition of g and the conjugacy class of w. It generalizes the formula of the Euler characteristic of Springer fibers for type A.

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KW - Deligne–Lusztig variety

KW - Euler characteristic

KW - Springer fiber

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