Rigged configuration bijection and proof of the X = M conjecture for nonexceptional affine types
- Author(s): Okado, M;
- Schilling, A;
- Scrimshaw, T
- et al.
Published Web Locationhttps://doi.org/10.1016/j.jalgebra.2018.08.031
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.