Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types

TL;DR

This paper demonstrates that for large-rank nonexceptional affine algebras, the fermionic formula depends solely on the attachment of node 0 and can be expressed via type A formulas with Littlewood-Richardson coefficients, settling the X=M conjecture.

Contribution

It establishes a simplified dependence of fermionic formulas on Dynkin diagram attachment and expresses non-type A formulas as sums of type A formulas, confirming the X=M conjecture in large rank.

Findings

Fermionic formula depends only on node 0 attachment in large rank

Non-type A fermionic formulas can be expressed as sums of type A formulas

X=M conjecture is settled under large rank hypothesis

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 math.CO/9901037 and arXiv:1002.3715 we settle the X=M conjecture under the large rank hypothesis.