The geometry of some generalized affine Springer fibers

2017/10/30 by Chi, Jingren
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1710.11243

Abstract

We study basic geometric properties of some group analogue of affine Springer fibers and compare with the classical Lie algebra affine Springer fibers. The main purpose is to formulate a conjecture that relates the number of irreducible components of such varieties for a reductive group G to certain weight multiplicities defined by the Langlands dual group G. We prove our conjecture in the case of unramified conjugacy class.

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• The affine Springer fiber-sheaf correspondence
• Affine Springer fibers and depth zero L-packets
• Dimension des fibres de Springer affines pour les groupes