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 $${\mathcal{Q}}$$ -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 $${\mathcal{Q}}$$ -operators can be identified with the Q-functions, which appear in the Nested Bethe Ansatz.