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The geometry of some generalized affine Springer fibers (1710.11243v3)
Published 30 Oct 2017 in math.AG, math.NT, and math.RT
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 $\hat{G}$. We prove our conjecture in the case of unramified conjugacy class.