Unimodality of the distribution of Betti numbers for some Springer fibers

Lucas Fresse; Ronit Mansour; Anna Melnikov

doi:10.1016/j.jalgebra.2013.05.018

Unimodality of the distribution of Betti numbers for some Springer fibers

Lucas Fresse, Ronit Mansour, Anna Melnikov

Department of Mathematics

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

Abstract

In this paper, we compute the Betti numbers of the Springer fibers over nilpotent elements u∈gln(C) of Jordan forms (a, b), (a, b, 1), (a, ^1b), and (²², ^1b). We show that in all these cases the distribution of Betti numbers is unimodal. In the first two cases, we also identify the type of the Springer representations on the cohomology spaces.

Original language	English
Pages (from-to)	284-304
Number of pages	21
Journal	Journal of Algebra
Volume	391
DOIs	https://doi.org/10.1016/j.jalgebra.2013.05.018
State	Published - 1 Oct 2013

Bibliographical note

Funding Information:
The first two authors are partially supported by the ISF Grant No. 882/10 .

Keywords

Betti numbers
Springer fibers
Springer representations
Unimodality

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2013.05.018

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abstract = "In this paper, we compute the Betti numbers of the Springer fibers over nilpotent elements u∈gln(C) of Jordan forms (a, b), (a, b, 1), (a, 1b), and (22, 1b). We show that in all these cases the distribution of Betti numbers is unimodal. In the first two cases, we also identify the type of the Springer representations on the cohomology spaces.",

keywords = "Betti numbers, Springer fibers, Springer representations, Unimodality",

author = "Lucas Fresse and Ronit Mansour and Anna Melnikov",

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AU - Mansour, Ronit

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N2 - In this paper, we compute the Betti numbers of the Springer fibers over nilpotent elements u∈gln(C) of Jordan forms (a, b), (a, b, 1), (a, 1b), and (22, 1b). We show that in all these cases the distribution of Betti numbers is unimodal. In the first two cases, we also identify the type of the Springer representations on the cohomology spaces.

AB - In this paper, we compute the Betti numbers of the Springer fibers over nilpotent elements u∈gln(C) of Jordan forms (a, b), (a, b, 1), (a, 1b), and (22, 1b). We show that in all these cases the distribution of Betti numbers is unimodal. In the first two cases, we also identify the type of the Springer representations on the cohomology spaces.

KW - Betti numbers

KW - Springer fibers

KW - Springer representations

KW - Unimodality

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JO - Journal of Algebra

JF - Journal of Algebra

ER -

Unimodality of the distribution of Betti numbers for some Springer fibers

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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