University of Sydney Algebra Seminar

Travis Scrimshaw (The University of Queensland)

Friday 4 May, 12-1pm, Place: Carslaw 375

Rigged configuration bijection for nonexceptional affine types

Kerov, Kirillov, and Reshetikhin developed combinatorial objects called rigged configurations to parameterise solutions to the Bethe Ansatz for Heisenberg spin chains and developed a bijection with classically irreducible components in a tensor product of finite-dimensional representations of the affine special linear Lie algebra. In this talk, we give a generalisation of the KKR bijection to all nonexceptional affine types by using Kashiwara’s theory of crystal bases and virtual crystals. In doing so, we give a combinatorial proof of the X = M conjecture of Hatayama et al. in all nonexceptional affine types. This is joint work with Masato Okado and Anne Schilling.