On the structure of smooth components of Springer fibers

Lucas Fresse; Anna Melnikov; Sammar Sakas-Obeid

doi:10.1090/S0002-9939-2015-12460-4

On the structure of smooth components of Springer fibers

Lucas Fresse, Anna Melnikov, Sammar Sakas-Obeid

Department of Mathematics

University of Haifa

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

Abstract

The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.

Original language	American English
Pages (from-to)	2301-2315
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	143
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-2015-12460-4
State	Published - 2015

Keywords

Betti numbers
Components of a Springer fiber
Flag manifolds
Grassmannian varieties
Iterated bundles

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

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10.1090/S0002-9939-2015-12460-4

Cite this

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abstract = "The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincar{\'e} polynomials.",

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AB - The aim of this paper is to study the structure of the smooth irreducible components of the Springer fibers associated to nilpotent endomorphisms of nilpotency order 2. Relying on its combinatorial interpretation in terms of standard Young tableaux, we show that each smooth component has a structure of iterated bundle of Grassmannian varieties, with explicit base. Using this description, we then classify the smooth components according to their Poincaré polynomials.

KW - Betti numbers

KW - Components of a Springer fiber

KW - Flag manifolds

KW - Grassmannian varieties

KW - Iterated bundles

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On the structure of smooth components of Springer fibers

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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