Rigged Configurations and Kashiwara Operators

Abstract

For types $A_n^{(1)}$ and $D_n^{(1)}$ we prove that the rigged configuration bijection intertwines the classical Kashiwara operators on tensor products of the arbitrary Kirillov-Reshetikhin crystals and the set of the rigged configurations.

v2: 108 pages, the author's final version for publication, Proposition 33 added, Section 7.3 partially reworked; v3: published version (Special Issue in honor of Anatol Kirillov and Tetsuji Miwa)

References in corpus (9)

• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• AGT conjecture and Integrable structure of Conformal field theory for c=1
• X=M for symmetric powers
• Superconformal field theory and Jack superpolynomials
• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• Kirillov--Schilling--Shimozono bijection as energy functions of crystals
• KKR type bijection for the exceptional affine algebra E_6^{(1)}
• Baker-Akhiezer functions and generalised Macdonald-Mehta integrals
• Ultradiscrete Soliton Systems and Combinatorial Representation Theory

Cited by in corpus (11)

• Soliton decomposition of the Box-Ball System
• Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations
• A rigged configuration model for $B(\infty )$
• 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
• Type $D_n^{(1)}$ rigged configuration bijection
• Rigged configurations for all symmetrizable types
• Rigged configurations and the $\ast$-involution
• Rigged configurations and the $\ast$-involution for generalized Kac--Moody algebras
• An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_2^{(1)}$
• Rigged Configuration Descriptions of the Crystals B(infinity) and B(lambda) for Special Linear Lie Algebras