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15 September 2015 Baxter’s relations and spectra of quantum integrable models
Edward Frenkel, David Hernandez
Duke Math. J. 164(12): 2407-2460 (15 September 2015). DOI: 10.1215/00127094-3146282


Generalized Baxter’s relations on the transfer matrices (also known as Baxter’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 category O, introduced by Hernandez and Jimbo, involving infinite-dimensional representations, 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. Combining 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 postulated by Frenkel and Reshetikhin in 1998. We also obtain generalized Bethe ansatz equations for all untwisted quantum affine algebras.


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Edward Frenkel. David Hernandez. "Baxter’s relations and spectra of quantum integrable models." Duke Math. J. 164 (12) 2407 - 2460, 15 September 2015.


Received: 26 March 2014; Revised: 18 October 2014; Published: 15 September 2015
First available in Project Euclid: 16 September 2015

zbMATH: 1332.82022
MathSciNet: MR3397389
Digital Object Identifier: 10.1215/00127094-3146282

Primary: 81R50
Secondary: 82B23

Keywords: Baxter’s relations , Bethe ansatz equations , Grothendieck ring

Rights: Copyright © 2015 Duke University Press


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Vol.164 • No. 12 • 15 September 2015
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