Continued fractions and fermionic representations for characters of \(M(p,p')\) minimal models

DOI10.1007/BF00400138zbMath0846.05004arXivhep-th/9412030OpenAlexW3104185937MaRDI QIDQ1915194

Alexander Berkovich, Barry M. McCoy

Publication date: 29 September 1996

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9412030

zbMATH Keywords

conformal field theorycontinued fractionRogers-Ramanujan type identities\(q\)-binomial identitiesAndrews-Bailey transformationfermionic sum representations

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Model quantum field theories (81T10)

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Cites Work

• Quantization of the Drinfel'd-Sokolov reduction.
• Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities
• Hidden SL(n) symmetry in conformal field theories
• Verma modules over the Virasoro algebra
• Lie algebras and equations of Korteweg-de Vries type
• Infinite-dimensional Lie algebras, theta functions and modular forms
• Unitary representations of the Virasoro and super-Virasoro algebras
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Modular and conformal invariance constraints in representation theory of affine algebras
• Modular invariant partition functions in two dimensions
• Virasoro characters from Bethe equations for the critical ferromagnetic three-state Potts model
• The many faces of a character
• Fermionic counting of RSOS states and Virasoro character formulas for the unitary minimal series \(M(\nu,\nu+1)\): Exact results
• Spin-anisotropy commensurable chains. Quantum group symmetries and \(N=2\) SUSY
• Fermionic sum representations for conformal field theory characters
• DILOGARITHM IDENTITIES IN CONFORMAL FIELD THEORY
• DILOGARITHM IDENTITIES, FUSION RULES AND STRUCTURE CONSTANTS OF CFTs
• Virasoro Character Identities from the Andrews–Bailey Construction
• PATH SPACES AND $\mathcal W$ FUSION IN MINIMAL MODELS
• FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER MATRIX
• POLYNOMIAL IDENTITIES OF THE ROGERS-RAMANUJAN TYPE
• ON STATE COUNTING AND CHARACTERS
• A-D-E POLYNOMIAL AND ROGERS-RAMANUJAN IDENTITIES
• A Combinatorial Generalization of the Rogers-Ramanujan Identities
• CRITICAL RSOS MODELS AND CONFORMAL FIELD THEORY
• Restricted solid-on-solid models connected with simply laced algebras and conformal field theory
• Structure of the Standard Modules for the Affine Lie Algebra 𝐴⁽¹⁾₁
• Modular invariant representations of infinite-dimensional Lie algebras and superalgebras
• THE ANNIHILATING IDEALS OF MINIMAL MODELS
• An Analytic Generalization of the Rogers-Ramanujan Identities for Odd Moduli
• Exceptional structure of the dilute A₃model: E₈and E₇Rogers-Ramanujan identities
• Some Identities in Combinatory Analysis