On the affine Springer fibers inside the invariant center of the small quantum group

2022/05/19 by Nicolas Hemelsoet, Hemelsoet, Nicolas, Oscar Kivinen +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Black Holes and Theoretical Physics

paper · pdf · doi:10.48550/arxiv.2205.09700

Abstract

Let \mathfraku_ζ^\vee denote the small quantum group associated with a simple Lie algebra \mathfrakg^\vee and a root of unity ζ. In [9], a geometric realization of Z(\mathfraku_ζ^\vee)^{G^\vee}, the G^\vee-invariant part of the center of \mathfraku_ζ^\vee, was proposed. We compute the dimension of the geometric subalgebra of the center and in the case where G=SL_n, we study a bigraded refinement of the result.

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