Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices

2010/08/31 by S. E. Derkachov, Sergey E. Derkachov, A. N. Manashov +1
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Quantum many-body systems #hep-th #nlin.SI

paper · pdf · doi:10.1007/s11005-011-0472-2

published as Lett.Math.Phys.97:185-202,2011 · 17 pages, typos fixed, references added, version accepted for publication in Lett. Math. Phys

openalex publication_date 2011/02/23 · arxiv created 2011/03/01 · arxiv updated 2011/07/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study properties of transfer matrices in the sl(N) spin chain models. The transfer matrices with an infinite dimensional auxiliary space are factorized into the product of N commuting Baxter Q-operators. We consider the transfer matrices with auxiliary spaces of a special type (including the finite dimensional ones). It is shown that they can be represented as the alternating sum over the transfer matrices with infinite dimensional auxiliary spaces. We show that certain combinations of the Baxter Q-operators can be identified with the Q-functions which appear in the Nested Bethe Ansatz.

Citations

• Baxter operators for the noncompact quantumsl(3) invariant spin chain
• Factorization of the transfer matrices for the quantumsell(2) spin chains and Baxter equation
• Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra
• Factorization of R -matrix and Baxter Q -operators for genericsl(N) spin chains
• Analytic Bethe ansatz and functional equations for Lie superalgebra