English

Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection

Quantum Algebra 2008-11-26 v1 Mathematical Physics math.MP

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.

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Cite

@article{arxiv.math/0601630,
  title  = {Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection},
  author = {Atsuo Kuniba and Masato Okado and Reiho Sakamoto and Taichiro Takagi and Yasuhiko Yamada},
  journal= {arXiv preprint arXiv:math/0601630},
  year   = {2008}
}

Comments

28 pages