Algebra Seminar: Scrimshaw -- Rigged configuration bijection for nonexceptional affine types

Travis Scrimshaw (The University of Queensland) 

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

Title: Rigged configuration bijection for nonexceptional affine types 

Abstract: 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.