2005/01/21 by Mark Shimozono, Shimozono, Mark
Mathematics · #05A30 #17B37 #81R10 #81R50 #82B23 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA #msc:05A30 #msc:17B37 #msc:81R10 #msc:81R50 #msc:82B23
paper · pdf · doi:10.48550/arxiv.math/0501353
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arxiv created 2005/01/21 · openalex publication_date 2005/01/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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).