On the X=M=K Conjecture

Abstract

In the large rank limit, for any nonexceptional affine algebra, the graded branching multiplicities known as one-dimensional sums, are conjectured to have a simple relationship with those of type A, which are known as generalized Kostka polynomials. This is called the X=M=K conjecture. It is proved for tensor products of the symmetric power Kirillov-Reshetikhin modules for all nonexceptional affine algebras except those whose Dynkin diagrams are isomorphic to that of untwisted affine type D near the zero node. Combined with results of Lecouvey, this realizes the above one-dimensional sums of affine type C, as affine Kazhdan-Lusztig polynomials (and conjecturally for type D).

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Cited by in corpus (3)

• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
• Ultradiscrete Soliton Systems and Combinatorial Representation Theory
• Quantization of branching coefficients for classical Lie groups