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arXiv · 1710.11243

The geometry of some generalized affine Springer fibers

Jingren Chi
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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.

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Jingren Chi. 2017-10-30. The geometry of some generalized affine Springer fibers. https://arxiv.org/abs/1710.11243

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