Analytic Bethe ansatz and functional relations related to tensor-like representations of type-II Lie superalgebrasB(r|s) andD(r|s)

1999/09/28 by Zengo Tsuboi
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1088/0305-4470/32/41/311

published as J. Phys. A: Math. Gen. 32 (1999) 7175-7206 · 45 pages

openalex publication_date 1999/09/28 · arxiv created 2009/11/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

An analytic Bethe ansatz is carried out related to tensor-like representations of the type-II Lie superalgebras B ( r | s ) = osp (2 r +1|2 s ) ( r 0 , s 1 ) and D ( r|s ) = osp (2 r|2s ) ( r 2 , s 1 ). We present eigenvalue formulae of transfer matrices in dressed vacuum forms (DVFs) labelled by Young (super) diagrams. A class of transfer matrix functional relations ( T -system) is discussed. In particular for the B (0| s ) = osp (1|2 s ) ( s 1 ) case, a complete set of functional relations is proposed by using duality among DVFs.

Citations

• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)
• AN ALGEBRAIC APPROACH TO VERTEX MODELS AND TRANSFER MATRIX SPECTRA
• Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1
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