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

University of Haifa

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	American 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

Keywords

Betti numbers
Springer fibers
Springer representations
Unimodality

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1016/j.jalgebra.2013.05.018

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title = "Unimodality of the distribution of Betti numbers for some Springer fibers",

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",

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

year = "2013",

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doi = "10.1016/j.jalgebra.2013.05.018",

language = "American English",

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AU - Fresse, Lucas

AU - Mansour, Ronit

AU - Melnikov, Anna

N1 - Funding Information: The first two authors are partially supported by the ISF Grant No. 882/10 .

PY - 2013/10/1

Y1 - 2013/10/1

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

UR - http://www.scopus.com/inward/record.url?scp=84880795365&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2013.05.018

DO - 10.1016/j.jalgebra.2013.05.018

M3 - Article

SN - 0021-8693

VL - 391

SP - 284

EP - 304

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Unimodality of the distribution of Betti numbers for some Springer fibers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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