KKR type bijection for the exceptional affine algebra E_6^{(1)}

Abstract

For the exceptional affine type E_6^{(1)} we establish a statistic-preserving bijection between the highest weight paths consisting of the simplest Kirillov-Reshetikhin crystal and the rigged configurations. The algorithm only uses the structure of the crystal graph, hence could also be applied to other exceptional types.

16 pages; typos fixed

References in corpus (7)

• The A^{(1)}_M automata related to crystals of symmetric tensors
• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• X=M for symmetric powers
• Tau functions in combinatorial Bethe ansatz
• The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture
• Affine structures and a tableau model for E_6 crystals
• Weyl modules, Demazure modules and finite crystals for non-simply laced type

Cited by in corpus (4)

• Affine crystal structure on rigged configurations of type D_n^(1)
• Rigged Configurations and Kashiwara Operators
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Crystal structure on rigged configurations and the filling map