Jianronmg Li: "Geometric cactus groups and geometric crystals"
Abstract:
In this talk (based on joint work with Arkady Berenstein and Jacob Greenstein), we will define a geometric cactus group for each split reductive group. Unipotent bicrystals and geometric crystals were introduced by Arkady Berenstein and David Kazhdan. We will show that geometric cactus groups act on unipotent bicrystals. Therefore they act on geometric crystals. We will show that geometric cactus group actions preserve the potentials on unipotent bicrystals. Moreover, the tropicalizations of certain geometric cactus group actions coincide with the Bender-Knuth moves on Gelfand-Tsetlin patterns studied by Arkady Berenstein and Anatol N. Kirillov.
Crystal Hoyt: "Representations of sl(infinity) and category O for gl(m|n)"
Abstract:
The Lie algebra sl(infinity) is a direct limit of the Lie algebras sl(n). Brundan, Losev and Webster showed that the integral category O for gl(m|n) has a categorical sl(infinity)-action, where the action is defined via certain translation functors. The (reduced) Grothendieck group inherits a natural sl(infinity)-module structure. In this talk, we will describe the structure of this module by giving its socle filtration.
This is a joint work with I. Penkov, V. Serganova
Shifra Reif: "Factorization of tensor products of modules over infinite dimensional Lie algebras"
Abstract:
A classical theorem of Rajan states that a tensor product of simple finite-dimensional modules over a simple Lie algebra admits unique factorization. In this talk, we shall discuss various types of infinite dimensional Lie algebras and the factorization of tensor products for these algebras. Joint with Venkatesh.
Maria Gorelik: "Arakawa's Theorem for osp(1|2n)"
Abstract:
In this talk I will discuss a proof of Arakawa's Theorem for osp(1|2n). This is a joint work with V. Serganova.