From Characters to Quantum (Super)Spin Chains via Fusion

Abstract

We give an elementary proof of the Bazhanov-Reshetikhin determinant formula for rational transfer matrices of the twisted quantum super-spin chains associated with the gl(K|M) algebra. This formula describes the most general fusion of transfer matrices in symmetric representations into arbitrary finite dimensional representations of the algebra and is at the heart of analytical Bethe ansatz approach. Our technique represents a systematic generalization of the usual Jacobi-Trudi formula for characters to its quantum analogue using certain group derivatives.

11 figures, references added

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• Baxter's Q-operators and operatorial Backlund flow for quantum (super)-spin chains
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• QQ-system and Weyl-type transfer matrices in integrable SO(2r) spin chains
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• Fusion hierarchies for N = 4 superYang-Mills theory
• First-principles derivation of the AdS/CFT Y-systems
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• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators
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• Structure of the string R-matrix
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• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
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• Quantum Gaudin model and classical KP hierarchy
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system