Components of affine Springer fibers

2016/09/16 by Tsai, Cheng-Chiang
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1609.05176

Abstract

Let G be a connected split reductive group over a field of characteristic zero or sufficiently large characteristic, γ₀∈(LieG)((t)) be any topologically nilpotent regular semisimple element, and γ=tγ₀. Using methods from p-adic orbital integrals, we show that the number of components of the Iwahori affine Springer fiber over γ modulo Z_G((t))(γ) is equal to the order of the Weyl group.

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