On the topology of components of some Springer fibers and their relation to Kazhdan-Lusztig theory

2002/04/18 by Francis Fung, Francis Y. C. Fung, Fung, Francis
Mathematics · #20C08 (primary) #20G05 (secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Representation Theory (math.RT) #math.RT #msc:20C08 #msc:20G05

paper · pdf · doi:10.48550/arxiv.math/0204224

This work has been submitted to Advances in Mathematics (Academic Press) for possible publication.

arxiv created 2002/04/18 · openalex publication_date 2002/04/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the irreducible components of Springer fibers for hook and two-row nilpotent elements of gl_n(C) as iterated bundles of flag manifolds and Grassmannians. We then relate the topology (in particular, the intersection homology Poincare' polynomials) of the intersections of these components with the inner products of the Kazhdan-Lusztig basis elements of irreducible representations of the rational Iwahori-Hecke algebra of type A corresponding to the hook and two-row Young shapes.

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