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

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.

60 pages, notation simplified

References in corpus (21)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• A Shortcut to the Q-Operator
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• Hidden Grassmann structure in the XXZ model
• Baxter Q-Operators and Representations of Yangians
• Baxter's Q-operators for supersymmetric spin chains
• Complete 1-loop test of AdS/CFT
• Pseudo-differential equations, and the Bethe Ansatz for the classical Lie algebras
• Q-systems as cluster algebras II: Cartan matrix of finite type and the polynomial property
• Wronskian Solution for AdS/CFT Y-system
• Quantization of the Gaudin System
• From Characters to Quantum (Super)Spin Chains via Fusion
• The Baxter's Q-operator for the W-algebra $W_N$
• Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Discrete Hirota dynamics for AdS/CFT
• Integrability and the AdS/CFT correspondence
• Noncompact sl(N) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite dimensional transfer matrices
• Nonlinear Integral Equations for Thermodynamics of the U_{q}(\hat{sl(r+1)}) Perk-Schultz Model
• Rational semistandard tableaux and character formula for the Lie superalgebra ${\widehat{\mathfrak{gl}}}_{\infty |\infty }$

Cited by in corpus (27)

• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• T-system on T-hook: Grassmannian Solution and Twisted Quantum Spectral Curve
• Solving the AdS/CFT Y-system
• Conformal algebra: R-matrix and star-triangle relation
• Fast analytic solver of rational Bethe equations
• Multiple zeta functions and double wrapping in planar N=4 SYM
• Classical tau-function for quantum spin chains
• Monodromy Bootstrap for SU(2|2) Quantum Spectral Curves: From Hubbard model to AdS3/CFT2
• The full spectrum of AdS5/CFT4 I: Representation theory and one-loop Q-system
• Quantum groups and functional relations for higher rank
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Asymptotic representations and q-oscillator solutions of the graded Yang-Baxter equation related to Baxter Q-operators
• Q-systems with boundary parameters
• Dissipation-driven integrable fermionic systems: from graded Yangians to exact nonequilibrium steady states
• Completeness of Wronskian Bethe equations for rational gl(m|n) spin chains
• Supersymmetric quantum spin chains and classical integrable systems
• On the calculation of the correlation functions of the ${\mathfrak{sl}}_3$-model by means of the reduced qKZ equation
• Universal Baxter TQ-relations for open boundary quantum integrable systems
• Quantum groups, Verma modules and $q$-oscillators: General linear case
• The $A_m^{(1)}$ Q-system
• Evaluation of the operatorial Q-system for non-compact super spin chains
• Folding QQ-relations and transfer matrix eigenvalues: towards a unified approach to Bethe ansatz for super spin chains
• Quantum groups and functional relations for arbitrary rank
• Transfer matrices of rational spin chains via novel BGG-type resolutions
• The complete unitary dual of non-compact Lie superalgebra su(p,q|m) via the generalised oscillator formalism, and non-compact Young diagrams
• Character Formulas for Kirillov-Reshetikhin Modules via Folding of Supercharacters of $\mathfrak{gl}(M|N)$
• Boson-Fermion correspondence, QQ-relations and Wronskian solutions of the T-system