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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.

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