Skip to main content
eScholarship
Open Access Publications from the University of California

UC Davis

UC Davis Previously Published Works bannerUC Davis

Rigged configuration bijection and proof of the X = M conjecture for nonexceptional affine types

  • Author(s): Okado, M
  • Schilling, A
  • Scrimshaw, T
  • et al.
Abstract

We establish a bijection between rigged configurations and highest weight elements of a tensor product of Kirillov–Reshetikhin crystals for all nonexceptional types. A key idea for the proof is to embed both objects into bigger sets for simply-laced types An(1) or Dn(1), whose bijections have already been established. As a consequence we settle the X=M conjecture in full generality for nonexceptional types. Furthermore, the bijection extends to a classical crystal isomorphism and sends the combinatorial R-matrix to the identity map on rigged configurations.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View