On the X=M=K Conjecture

Details On the X=M=K Conjecture On the X=M=K Conjecture

Publishing date

2005-01-21

URL

arxiv.org/abs/math/0501353v1

Science

Mathematics

Field

Combinatorics

Additional info

requires the provided style file rcyoungtab.sty

Type

Scientific paper

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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