Donna Testerman (EPFL) Multiplicity free representations of simple algebraic groups
Let G be a simple algebraic group defined over an algebraically closed field k and V an irreducible kG-module. One is interested in the action of certain simple closed infinite subgroups H of G on the module V. The literature is rich, and includes work of Dynkin, Seitz, Howe, Koike-Terada and others. Here we consider those modules V whose restriction to a G-irreducible subgroup H has non-isomorphic composition factors. When G is of classical type defined over kof characteristic zero and H is (a quotient of) SL(m,k), work of Liebeck-Seitz-Testerman gives a complete classification. Their proof was based upon induction on the rank of H. In recent joint work with Aluna Rizzoli, we treat the case where G = SL(n,k) over k of characteristic p , and H is the principal SL2 subgroup in G, which settles the base case for an inductive argument in positive characteristic for H = SL(m,k) and G of classical type.
Meinolf Geck (Stuttgart) Canonical structure constants for simple Lie algebras
TBC
George Lusztig (MIT) Distinguished strata in reductive groups
We extend the Bala-Carter definition of distinguished unipotent classes to the case of strata of a reductive group.
Jian-yi Shi (ECNU) Reflection length and reflection ordering on the group G(m,p,n)
TBC
Britta Späth (Wuppertal) On the McKay Conjecture
John McKay’s Conjecture (from 1971) predicts that, for any finite group G and prime l, the number of complex irreducible representations of G with a degree not divisible by l is controlled by the normaliser of a Sylow l-subgroup of G. By work of Isaacs, Malle and Navarro this conjecture was reduced to a statement on finite quasi-simple groups and their representation theory. After a series of results by various authors it is sufficient to verify a statement on finite Spin groups. In the talk I will report on recent progress. In joint work with Marc Cabanes we analyse the representation theory of a new subgroup of those Spin groups.
Simon Riche (Clermont Auvergne) Affine Hecke category and modular representations of reductive groups
In this talk I will explain joint work with Roman Bezrukavnikov where we identify three possible categorical counterparts of the affine Hecke algebra associated with a reductive algebraic group: one in terms of equivariant coherent sheaves on the Steinberg variety, one in terms of Harish-Chandra bimodules, and one in terms of constructible sheaves on the affine flag variety of the Langlands dual group. We will motivate this construction from the representation theory of reductive groups, and explain an application to this question, namely the proof of a conjecture by Finkelberg-Mirkovic.
Ana Paula Santana (Coimbra) Borel-Schur algebras and projective resolutions
TBC
Richard Green (Colorado Boulder) Quasiparabolic sets and Macdonald representations
TBC
Bethany Marsh (Leeds) Cluster presentations of Weyl groups and braid groups
TBC
Carlos André (Lisbon) Supercharacters of adjoint groups of radical rings and related subgroups
TBC