Wronskian solutions of the T-, Q- and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)

2011/09/30 by Zengo Tsuboi · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Basis (linear algebra) #Combinatorics #Discrete mathematics #Geometry #Hook #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #Real line #Superalgebra #Wronskian #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2013.01.007

published as Nuclear Physics B 870 [FS] (2013) 92-137 · 60 pages, notation simplified

openalex publication_date 2013/01/18 · arxiv created 2013/02/08 · arxiv updated 2013/02/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In [Z.Tsuboi, Nucl. Phys. B 826 (2010) 399 [arXiv:0906.2039]], we proposed Wronskian-like solutions of the T-system for [M,N]-hook of the general linear superalgebra gl(M|N). We have generalized these Wronskian-like solutions to the ones for the general T-hook, which is a union of [M1,N1]-hook and [M2,N2]-hook (M=M1+M1, N=N1+N2). These solutions are related to Weyl-type supercharacter formulas of infinite dimensional unitarizable modules of gl(M|N). Our solutions also include a Wronskian-like solution discussed in [N.Gromov, V.Kazakov, S.Leurent, Z.Tsuboi, JHEP 1101 (2011) 155 [arXiv:1010.2720]] in relation to the AdS5/CFT4 spectral problem.

Citations

• Solutions of the T-system and Baxter equations for supersymmetric spin chains
• Wronskian solution for AdS/CFT Y-system
• Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)
• Analytic Bethe ansatz and functional equations associated with any simple root systems of the Lie superalgebra sl(r+1∣s+1)
• Symmetrizable quantum affine superalgebras and their representations
• Analytic Bethe ansatz and functional relations related to tensor-like representations of type-II Lie superalgebrasB(r|s) andD(r|s)
• Integrable Structure of Conformal Field Theory III. The Yang-Baxter Relation
• Analytic Bethe ansatz related to the Lie superalgebra C(s)
• Noncompact sl(N) Spin Chains: BGG-Resolution, Q-Operators and Alternating Sum Representation for Finite-Dimensional Transfer Matrices
• Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra
• Nonlinear integral equations for complex affine Toda models associated with simply laced Lie algebras
• Analytic Bethe ansatz and functional equations for Lie superalgebra

Cited by

• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators
• On the calculation of the correlation functions of the s l 3 -model by means of the reduced qKZ equation