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

An analytic Bethe ansatz is carried out related to tensor-like representations of the type-II Lie superalgebras B(r|s) = osp(2r+1|2s) (r0, s1) and D(r|s) = osp(2r|2s) (r2, s1). 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|2s) (s1) case, a complete set of functional relations is proposed by using duality among DVFs.

[1]  Z. Tsuboi.  Analytic Bethe ansatz related to the Lie superalgebra C(s) , 1999, 0911.5390.

[2]  A. Fujii,et al.  Anti-symmetrically fused model and non-linear integral equations in the three-state Uimin-Sutherland model , 1998, cond-mat/9811234.

[3]  Z. Tsuboi.  Analytic Bethe ansatz related to a one-parameter family of finite-dimensional representations of the Lie superalgebra , 1998, 0911.5389.

[4]  J. Suzuki,et al.  From fusion hierarchy to excited state TBA , 1997, hep-th/9707074.

[5]  Z. Tsuboi.  Analytic Bethe ansatz and functional equations for Lie superalgebra , 1997, 0911.5386.

[6]  Ovidiu Lipan,et al.  Quantum Integrable Models and Discrete Classical Hirota Equations , 1997 .

[7]  M. J. Martins,et al.  The algebraic Bethe ansatz for rational braid-monoid lattice models , 1997, hep-th/9703023.

[8]  Z. Tsuboi.  Solutions of Discretized Affine Toda Field Equations for A n (1) , B n (1) , C n (1) , D n (1) , A n (2) and D n+1 (2) , 1996, solv-int/9610011.

[9]  M. Batchelor,et al.  Spin excitations in the integrable open quantum group invariant supersymmetric t- J model , 1996, cond-mat/9611013.

[10]  J. V. Jeugt,et al.  On the Lie superalgebra embedding C(n+1)⊃B(0,n) and dimension formulas , 1996 .

[11]  A. Kuniba,et al.  Solutions of a discretized Toda field equation for from analytic Bethe ansatz , 1996, hep-th/9608002.

[12]  H. Frahm,et al.  Algebraic Bethe ansatz for gl(2, 1) invariant 36-vertex models , 1996, cond-mat/9604082.

[13]  M. J. Martins,et al.  One-parameter family of an integrable spl(2|1) vertex model: Algebraic Bethe ansatz and ground state structure , 1996, hep-th/9604072.

[14]  R. Hirota,et al.  Pfaffian and determinant solutions to a discretized Toda equation for , and , 1995, hep-th/9509039.

[15]  Y. Ohta,et al.  Quantum Jacobi-Trudi and Giambelli formulae for Uq(Br(1)) from the analytic Bethe ansatz , 1995, hep-th/9506167.

[16]  N. Reshetikhin,et al.  Quantum affine algebras and deformations of the Virasoro and 237-1237-1237-1 , 1995, q-alg/9505025.

[17]  J. Suzuki,et al.  Functional relations and analytic Bethe ansatz for twisted quantum affine algebras , 1994, hep-th/9408135.

[18]  Z. Maassarani.  Uqosp(2,2) lattice models , 1994, hep-th/9407032.

[19]  J. Suzuki,et al.  Analytic Bethe ansatz for fundamental representations of Yangians , 1994, hep-th/9406180.

[20]  M. J. Martins,et al.  A note on graded Yang-Baxter solutions as braid-monoid invariants , 1994, hep-th/9410071.

[21]  J. Suzuki.  Fusion Uq(G(1)2) vertex models and analytic Bethe ansätze , 1994, hep-th/9405201.

[22]  Masaki Kashiwara,et al.  Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras , 1994 .

[23]  H. Yamane.  Quantized Enveloping Algebras Associated with Simple Lie Superalgebras and Their Universal R -matrices , 1994 .

[24]  J. Suzuki,et al.  FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS II: APPLICATIONS , 1993, hep-th/9310060.

[25]  J. Suzuki,et al.  FUNCTIONAL RELATIONS IN SOLVABLE LATTICE MODELS I: FUNCTIONAL RELATIONS AND REPRESENTATION THEORY , 1993, hep-th/9309137.

[26]  Toshiki Nakashima,et al.  Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras , 1993 .

[27]  A. Foerster,et al.  Algebraic properties of the Bethe ansatz for an spl(2,1)-supersymmetric t- J model , 1993 .

[28]  Korepin,et al.  Higher conservation laws and algebraic Bethe Ansa-umltze for the supersymmetric t-J model. , 1992, Physical review. B, Condensed matter.

[29]  V. Korepin,et al.  New exactly solvable model of strongly correlated electrons motivated by high-Tc superconductivity. , 1992, Physical review letters.

[30]  P. Pearce,et al.  Conformal weights of RSOS lattice models and their fusion hierarchies , 1992 .

[31]  P. Martin,et al.  a Template for Quantum Spin Chain Spectra , 1992 .

[32]  T. Deguchi,et al.  AN ALGEBRAIC APPROACH TO VERTEX MODELS AND TRANSFER MATRIX SPECTRA , 1992 .

[33]  A. Bracken,et al.  Solution of the graded Yang-Baxter equation associated with the vector representation of Uq(osp(M/2n)) , 1991 .

[34]  N. Reshetikhin,et al.  Representations of Yangians and multiplicities of occurrence of the irreducible components of the tensor product of representations of simple Lie algebras , 1990 .

[35]  H. Saleur.  Quantum osp(1,2) and solutions of the graded Yang-Baxter equation , 1990 .

[36]  N. Reshetikhin,et al.  Restricted solid-on-solid models connected with simply laced algebras and conformal field theory , 1990 .

[37]  T. Deguchi,et al.  Quantum superalgebra Uqosp(2,2) , 1990 .

[38]  N. Reshetikhin,et al.  Universal R-matrix of the quantum superalgebra osp(2 | 1) , 1989 .

[39]  V. Bazhanov,et al.  Trigonometric solutions of triangle equations. Simple lie superalgebras , 1987 .

[40]  N. Reshetikhin.  The spectrum of the transfer matrices connected with Kac-Moody algebras , 1987 .

[41]  N. Reshetikhin,et al.  Towards the classification of completely integrable quantum field theories (the Bethe-Ansatz associated with dynkin diagrams and their automorphisms) , 1987 .

[42]  V. Drinfeld.  A New realization of Yangians and quantized affine algebras , 1987 .

[43]  P. Kulish.  Integrable graded magnets , 1986 .

[44]  P. Wiegmann,et al.  Factorized S Matrix and the Bethe Ansatz for Simple Lie Groups , 1986 .

[45]  P. Duxbury,et al.  Low-temperature series analysis of multilayer adsorption at surfaces , 1985 .

[46]  A. Sciarrino,et al.  Representations of OSp(M/2n) and Young supertableaux , 1985 .

[47]  P. Jarvis,et al.  Representations of orthosymplectic superalgebras. II. Young diagrams and weight space techniques , 1984 .

[48]  Evgeny Sklyanin,et al.  Solutions of the Yang-Baxter equation , 1982 .

[49]  R. Hirota.  Discrete Analogue of a Generalized Toda Equation , 1981 .

[50]  N. Reshetikhin,et al.  Yang-Baxter equation and representation theory: I , 1981 .

[51]  Itzhak Bars,et al.  Dimension and Character Formulas for Lie Supergroups , 1981 .

[52]  Victor G. Kac,et al.  Representations of classical lie superalgebras , 1978 .