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

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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.

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Authors and Affiliations

  1. St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, Fontanka 27, 191023, St. Petersburg, Russia

    Sergey E. Derkachov

  2. Institute for Theoretical Physics, University of Regensburg, 93040, Regensburg, Germany

    Alexander N. Manashov

  3. Department of Theoretical Physics, Sankt-Petersburg University, St. Petersburg, Russia

    Alexander N. Manashov

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  1. Sergey E. Derkachov
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  2. Alexander N. Manashov
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Correspondence to Sergey E. Derkachov.

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Derkachov, S.E., Manashov, A.N. Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices. Lett Math Phys 97, 185–202 (2011). https://doi.org/10.1007/s11005-011-0472-2

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