On the structure of smooth components of Springer fibers

Fresse, Lucas; Melnikov, Anna; Sakas-Obeid, Sammar

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

On the structure of smooth components of Springer fibers
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by Lucas Fresse, Anna Melnikov and Sammar Sakas-Obeid

Proc. Amer. Math. Soc. 143 (2015), 2301-2315

DOI: https://doi.org/10.1090/S0002-9939-2015-12460-4

Published electronically: January 14, 2015

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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 Poincaré polynomials.

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