Composition factors for the Springer resolution

2014/07/19 by Vladimir Shchigolev, Shchigolev, Vladimir
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1407.5169

openalex publication_date 2014/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let π:\widetilde\mathcal N→\mathcal N be the Springer resolution of the nilpotent cone for a semisimple connected algebraic group G over \mathbb C and k be an arbitrary field. What happens to π_*k[dim\mathcal N] if the decomposition theorem fails for it? We show that in this case, some additional (with respect to the case \rm char k=0) composition factors of this direct image in the (abelian) category of perverse sheaves may emerge. These factors emerge from the Z_G(x)/Z_G(x)⁰-composition factors of the radicals of certain intersection forms and from that of the top comohologies of Springer fibres (in the non-semisimple case).

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