Journal
ANNALES HENRI POINCARE
Volume 18, Issue 8, Pages 2543-2579Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00023-017-0577-y
Keywords
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Funding
- Russian Science Foundation [16-11-10316]
- JSPS KAKENHI [JP16K05183]
- Simons Foundation [353831]
- Grants-in-Aid for Scientific Research [16K05183] Funding Source: KAKEN
- Russian Science Foundation [16-11-10316] Funding Source: Russian Science Foundation
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We introduce and study a category of modules of the Borel subalgebra of a quantum affine algebra , where the commutative algebra of Drinfeld generators , corresponding to Cartan currents, has finitely many characteristic values. This category is a natural extension of the category of finite-dimensional 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 . Among them, we find the Baxter operators and operators satisfying relations of the form . 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 operators acting in an arbitrary finite-dimensional representation of .
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