Abstract

This is based on arXiv:2408.02485, joint with Bezrukavnikov. We construct certain functors on categories ofrepresentations of rational Cherednik algebras associated with symmetric groups in zero and large positivecharacteristic. Our functors are indexed by pairs of a partition and a rational number, the slope. For a givenslope, the functors give an action of the positive half of the Heisenberg Lie algebra, while when the slopevaries and the characteristic is positive we get a categorical action of the positive half of the elliptic Hallalgebra. In this talk I will define rational Cherednik algebras and their categories of modular representations,state our main result and explain how our construction affinizes a version of the Steinberg tensor producttheorem for the quantum GLn. Time permitting, I’ll say a couple of words about the construction, a categorical representation of the positive half of the elliptic Hall algebra, etc.