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Baxter Q-Operators and Representations of Yangians | | Vladimir V. Bazhanov
; Rouven Frassek
; Tomasz Lukowski
; Carlo Meneghelli
; Matthias Staudacher
; | | Date: |
18 Oct 2010 | | Abstract: | We develop a new approach to Baxter Q-operators by relating them to the
theory of Yangians, which are the simplest examples for quantum groups. Here we
open up a new chapter in this theory and study certain degenerate solutions of
the Yang-Baxter equation connected with harmonic oscillator algebras. These
infinite-state solutions of the Yang-Baxter equation serve as elementary,
"partonic" building blocks for other solutions via the standard fusion
procedure. As a first example of the method we consider sl(n) compact spin
chains and derive the full hierarchy of operatorial functional equations for
all related commuting transfer matrices and Q-operators. This leads to a
systematic and transparent solution of these chains, where the nested Bethe
equations are derived in an entirely algebraic fashion, without any reference
to the traditional Bethe ansatz techniques. | | Source: | arXiv, 1010.3699 | | Services: | Forum | Review | PDF | Favorites | |
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