Stable rigged configurations and Littlewood―Richardson tableaux

Abstract

For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type $A$ can be expressed as a sum of that of type $A$ with Littlewood–Richardson coefficients. Combining this result with theorems of Kirillov–Schilling–Shimozono and Lecouvey–Okado–Shimozono, we settle the $X=M$ conjecture under the large rank hypothesis.

Keywords

• affine crystals
• rigged configurations
• littlewood―richardson tableaux
• fermionic formula
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]