TY - JOUR
T1 - Finite Type Modules and Bethe Ansatz Equations
AU - Feigin, Boris
AU - Jimbo, Michio
AU - Miwa, Tetsuji
AU - Mukhin, Eugene
N1 - Publisher Copyright:
© 2017, Springer International Publishing.
PY - 2017/8/1
Y1 - 2017/8/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85017129329&partnerID=8YFLogxK
U2 - 10.1007/s00023-017-0577-y
DO - 10.1007/s00023-017-0577-y
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AN - SCOPUS:85017129329
SN - 1424-0637
VL - 18
SP - 2543
EP - 2579
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 8
ER -