Geometry and cohomology of compactified Deligne--Lusztig varieties

2024/03/01 by Wang, Yingying
#14G17 #20G40 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2403.00979

Abstract

For connected reductive groups together with a Frobenius root F that preserves the set of simple reflections, we show that for every tuple (w₁,…, w_r) of Weyl group elements there exists a minimal length element in an F-conjugacy class in W such that the cohomology of the structure sheaf and the canonical sheaf for the associated compactified Deligne--Lusztig varieties are isomorphic respectively.

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