A BURGE TREE OF VIRASORO-TYPE POLYNOMIAL IDENTITIES

DOI10.1142/S0217751X98002328zbMath0939.81006arXivq-alg/9710025MaRDI QIDQ4261986

Keith S. M. Lee, Trevor A. Welsh, Omar Foda

Publication date: 19 September 1999

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-alg/9710025

zbMATH Keywords

combinatorial identitypartition pairssummation formulaVirasoro characters\(q\)-polynomial identities

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Virasoro and related algebras (17B68) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10)

Related Items

AGT, burge pairs and minimal models ⋮ From topological strings to minimal models ⋮ AGT, \(N\)-Burge partitions and \( {\mathcal{W}}_N \) minimal models ⋮ Bressoud's identities for even moduli. New companions and related positivity results ⋮ The 𝐴₂ Andrews–Gordon identities and cylindric partitions ⋮ Off-critical local height probabilities on a plane and critical partition functions on a cylinder ⋮ The generalized Borwein conjecture. II: Refined \(q\)-trinomial coefficients ⋮ \(\widehat{\mathfrak{sl}}(n)_N\) WZW conformal blocks from \(SU(N)\) instanton partition functions on \(\mathbb{C}^2/\mathbb{Z}_N\) ⋮ Positivity preserving transformations for 𝑞-binomial coefficients ⋮ q -Trinomial identities ⋮ Exclusion statistics in conformal field theory and the UCPF for WZW models.

Cites Work

• Further exact solutions of the eight-vertex SOS model and generalizations of the Rogers-Ramanujan identities
• Multiple series Rogers-Ramanujan type identities
• Eight-vertex SOS model and generalized Rogers-Ramanujan-type identities
• Combinatorics, Bethe Ansatz, and representations of the symmetric group
• Partitions with prescribed hook differences
• Infinite conformal symmetry in two-dimensional quantum field theory
• Rogers-Schur-Ramanujan type identities for the \(M(p,p')\) minimal models of conformal field theory
• Fermionic solution of the Andrews-Baxter-Forrester model. I: Unification of TBA and CTM methods.
• Fermionic solution of the Andrews-Baxter-Forrester model. II: Proof of Melzer's polynomial identities.
• Restricted partition pairs
• Exactly solvable SOS models. Local height probabilities and theta function identities
• A bijection which implies Melzer's polynomial identities: The \(\chi_{1,1}^{(p,p+1)}\) case
• Continued fractions and fermionic representations for characters of \(M(p,p')\) minimal models
• A new symmetrical combinatorial identity
• Virasoro Character Identities from the Andrews–Bailey Construction
• STRINGS, PATHS AND STANDARD TABLEAUX
• A proof of polynomial identities of type sl(n̂)1⊗sl(n̂)1/sl(n̂)2
• Cylindric Partitions
• Identities of the Rogers-Ramanujan Type