A uniform approach to soliton cellular automata using rigged configurations

Abstract

For soliton cellular automata, we give a uniform description and proofs of the solitons, the scattering rule of two solitons, and the phase shift using rigged configurations in a number of special cases. In particular, we prove these properties for the soliton cellular automata using $B^{r,1}$ when $r$ is adjacent to $0$ in the Dynkin diagram or there is a Dynkin diagram automorphism sending $r$ to $0$.

37 pages, 3 figures, 4 tables

References in corpus (12)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• X=M for symmetric powers
• Demazure structure inside Kirillov-Reshetikhin crystals
• Tau functions in combinatorial Bethe ansatz
• Perfect Crystals for U_q(D_4^{(3)})
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Relationships Between Two Approaches: Rigged Configurations and 10-Eliminations
• Scattering Rule in Soliton Cellular Automaton associated with Crystal Base of $U_q(D_4^{(3)})$
• Type $D_n^{(1)}$ rigged configuration bijection
• Rigged configurations as tropicalizations of loop Schur functions

Cited by in corpus (3)

• On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models
• Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices
• Kirillov-Reshetikhin crystals $B^{7,s}$ for type $E_7^{(1)}$