A rigged configuration model for $B(\infty )$

Abstract

We describe a combinatorial realization of the crystals $B(\infty )$ and $B(\lambda )$ using rigged configurations in all symmetrizable Kac-Moody types up to certain conditions. This includes all simply-laced types and all non-simply-laced finite and affine types.

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Cited by in corpus (13)

• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Rigged configurations and the $\ast$-involution
• Connecting marginally large tableaux and rigged configurations via crystals
• Virtualization map for the Littelmann path model
• Rigged configurations as tropicalizations of loop Schur functions
• Uniform description of the rigged configuration bijection
• Candidate for the crystal $B(-\infty )$ for the queer Lie superalgebra
• Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras
• Alcove path model for $B(\infty )$
• Virtual Crystals and Nakajima Monomials
• Rigged Configuration Descriptions of the Crystals B(infinity) and B(lambda) for Special Linear Lie Algebras
• A new description of the bicrystal $B(\infty )$ and the extended crystal