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SUMMARY:Categorical Heisenberg actions and modular representations of rati
 onal Cherednik algebras - Ivan  Losev (Yale University)
DTSTART:20250714T101500Z
DTEND:20250714T111500Z
UID:TALK233983@talks.cam.ac.uk
DESCRIPTION: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 posi
 tivecharacteristic. Our functors are indexed by pairs of a partition and a
  rational number\, the slope. For a givenslope\, the functors give an acti
 on of the positive half of the Heisenberg Lie algebra\, while when the slo
 pevaries and the characteristic is positive we get a categorical action of
  the positive half of the elliptic Hallalgebra.\nIn this talk I will defin
 e rational Cherednik algebras and their categories of modular representati
 ons\,state our main result and explain how our construction affinizes a ve
 rsion of the Steinberg tensor producttheorem for the quantum GLn.\nTime pe
 rmitting\, I&rsquo\;ll say a couple of words about the construction\, a ca
 tegorical representation of the positive half of the elliptic Hall algebra
 \, etc.
LOCATION:External
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