BAXTER'S RELATIONS AND SPECTRA OF QUANTUM INTEGRABLE MODELS

By E. Frenkel, D. Hernandez. 2013

149 citations recorded by the source corpus.

Generalized Baxter's relations on the transfer-matrices (also known as Bax- ter's TQ relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we interpret them as relations in the Grothendieck ring of the cate- gory O introduced by Jimbo and the second author in (HJ) involving infinite-dimensional representations constructed in (HJ), which we call here "prefundamental". We define the transfer-matrices associated to the prefundamental representations and prove that their eigenvalues on any finite-dimensional representation are polynomials up to a universal factor. These polynomials are the analogues of the celebrated Baxter polynomials. Com- bining these two results, we express the spectra of the transfer-matrices in the general quantum integrable systems associated to an arbitrary untwisted quantum affine algebra in terms of our generalized Baxter polynomials. This proves a conjecture of Reshetikhin and the first author formulated in 1998 (FR1). We also obtain generalized Bethe Ansatz equations for all untwisted quantum affine algebras.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e8882a7f4533e550705d91e22069588d7254aaac

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Citations in the corpus

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters (2015, background): “The latter is familiar from the study of lattice and massive integrable field theories in two dimensions [10, 20–23, 30–33, 35, 36, 38, 39, 53, 60, 109–115].”
Quantum Geometry and Quiver Gauge Theories (2013, methodology): “It looks like our formulation is T -Q dual (in a sense of [201]) to the results of the recent paper [94] on the category O of representations of the quantum affine algebras, at least for the finite dimensional gΓ.”
Yangians, quantum loop algebras and abelian difference equations (2013, background): “(resp. a power of q ) (see, e.g., [1, 4, 23]).”
Quiver W-algebras (2015, methodology): “omology (4d theory) or by equivariant elliptic cohomology (6d theory reduced on elliptic curve). Consequently, the geometric construction of K-theoretic W-algebra can be scaled to its Yangian version [1, 15, 16, 23] using cohomology and lifted to the elliptic version [24, 25] using elliptic cohomolo”