Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
classification
🧮 math.QA
math-phmath.MP
keywords
bijectioncombinatorialcrystalkerov-kirillov-reshetikhinalgorithmansatzassociatedautomaton
read the original abstract
The Kerov-Kirillov-Reshetikhin (KKR) bijection is the crux in proving fermionic formulas. It is defined by a combinatorial algorithm on rigged configurations and highest paths. We reformulate the KKR bijection as a vertex operator by purely using combinatorial R in crystal base theory. The result is viewed as a nested Bethe ansatz at q=0 as well as the direct and the inverse scattering (Gel'fand-Levitan) map in the associated soliton cellular automaton.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.