- Date: 2023-10-06 (Fri) 18:00 ~ 19:30, 2023-11-03 (Fri) 18:00 ~ 19:30
- Speaker: Alexey Sevastyanov (University of Aberdeen)
- Lecture 1: Algebraic group analogues of the Slodowy slices and the structure of the set of conjugacy classes in algebraic groups.
Abstract: In this lecture I shall introduce algebraic group analogues of the Slodowy slices and prove an analogue of the Kostant cross-section theorem for them. Then I shall discuss how these slices intersect the strata of the Lusztig partition. It is based on Sections 1.1-1.5 of my book "Q-W-algebras, Zhelobenko operators and a proof of De Concini-Kac-Procesi conjecture" (arXiv:2102.03208)
Lecture 2: Poisson q-W-algebras.
Abstract: In this lecture, using Poisson reduction technique and the theory of Poisson-Lie groups, I shall introduce Poisson structures on the algebraic group analogues of the Slodowy slices which have important applications in representation theory of quantum groups. An explicit formula for these Poisson structures will be given. It is based on Sections 4 and 5 of my paper "Algebraic group analogues of Slodowy slices and deformations of Poisson W–algebras", Int. Math. Res. Not. 2011 (2011), 1880–1925 and Section 3 of my paper "The structure of q-W algebras", Transf. Groups 25, no. 1 (2020), 279–304.
In both lectures I shall work over more general fields to cover the finite-dimensional and the affine case at the same time. Some familiarity with the theory of algebraic/Lie groups and Weyl group theory is assumed in Lecture 1, and with Poisson geometry in Lecture 2.