Fusion products of Kirillov-Reshetikhin modules and the X = M conjecture

Abstract

In this article, we show in the ADE case that the fusion product of Kirillov-Reshetikhin modules for a current algebra, whose character is expressed in terms of fermionic forms, can be constructed from one-dimensional modules by using Joseph functors. As a consequence, we obtain some identity between fermionic forms and Demazure operators. Since the same identity is also known to hold for one-dimensional sums of nonexceptional type, we can show from these results the X = M conjecture for type $A_n^{(1)}$ and $D_n^{(1)}$.

27 pages, added references and corrected typos

References in corpus (6)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas
• A pentagon of identities, graded tensor products and the Kirillov-Reshetikhin conjecture
• A bijection between type D_n^{(1)} crystals and rigged configurations
• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
• Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels

Cited by in corpus (2)

• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Demazure crystals and tensor products of perfect Kirillov-Reshetikhin crystals with various levels