The affine Springer fiber-sheaf correspondence

2022/04/01 by Gorsky, Eugene, Kivinen, Oscar, Oblomkov, Alexei · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2204.00303

Abstract

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the Langlands dual group. The construction uses affine Springer theory and can be thought of as an incarnation of 3d mirror symmetry. For the group GL_n, the corresponding partial resolution is Hilbⁿ(ℂ^×× ℂ). We also consider a quantization of this construction for homogeneous elements.

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