Noncompact sl(N) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite dimensional transfer matrices

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.

17 pages, typos fixed, references added, version accepted for publication in Lett. Math. Phys

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• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
• BGG complexes in singular infinitesimal character for type A
• Evaluation of the operatorial Q-system for non-compact super spin chains
• SO(d,1)-invariant Yang-Baxter operators and the dS/CFT correspondence
• Transfer matrices of rational spin chains via novel BGG-type resolutions
• Recursive properties of branching and BGG resolution