Finite Type Modules and Bethe Ansatz Equations

Boris Feigin, Michio Jimbo, Tetsuji Miwa, Eugene Mukhin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We introduce and study a category Obfin of modules of the Borel subalgebra Uqb of a quantum affine algebra Uqg, where the commutative algebra of Drinfeld generators hi , r, corresponding to Cartan currents, has finitely many characteristic values. This category is a natural extension of the category of finite-dimensional Uqg modules. In particular, we classify the irreducible objects, discuss their properties, and describe the combinatorics of the q-characters. We study transfer matrices corresponding to modules in Obfin. Among them, we find the Baxter Qi operators and Ti operators satisfying relations of the form TiQi= ∏ jQj+ ∏ kQk. We show that these operators are polynomials of the spectral parameter after a suitable normalization. This allows us to prove the Bethe ansatz equations for the zeroes of the eigenvalues of the Qi operators acting in an arbitrary finite-dimensional representation of Uqg.

Original languageEnglish
Pages (from-to)2543-2579
Number of pages37
JournalAnnales Henri Poincare
Volume18
Issue number8
DOIs
StatePublished - 1 Aug 2017
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2017, Springer International Publishing.

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