Cohomology of Commuting Varieties of Connected Compact Reductive Lie Groups

2016/08/05 by Henry Scher, Scher, Henry
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1608.01743

openalex publication_date 2016/08/05 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

We calculate the rational cohomology of the commuting variety X_{G, n} consisting of n-tuples of commuting elements of a compact reductive group G. This is done by studying a map from a related variety Y_{G, n}, which has easily calculated cohomology. The proof studies the fibers of the map and uses the Vietoris-Begle theorem to prove that the induced map on rational cohomology is an isomorphism.

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