A combinatorial proof of a partition identity related to the level 3 representations of a twisted affine lie algebra

DOI10.1080/00927879508825379zbMath0830.17012OpenAlexW2166603386MaRDI QIDQ4843201

Stefano Capparelli

Publication date: 10 September 1995

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879508825379

zbMATH Keywords

representationsaffine Lie algebrapartition identityintegrable highest weight modules

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (13)

Polynomial identities implying Capparelli's partition theorems ⋮ A unifying combinatorial approach to refined little Göllnitz and Capparelli's companion identities ⋮ Sequences, q-Multinomial Identities, Integer Partitions with Kinds, and Generalized Galois Numbers ⋮ The 3-state Potts model and Rogers-Ramanujan series ⋮ Some more identities of Kanade-Russell type derived using Rosengren's method ⋮ On the \(q\)-binomial identities involving the Legendre symbol modulo 3 ⋮ A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type ⋮ New infinite hierarchies of polynomial identities related to the Capparelli partition theorems ⋮ Elementary polynomial identities involving \(q\)-trinomial coefficients ⋮ A new companion to Capparelli's identities ⋮ Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities ⋮ Some partition and analytical identities arising from the Alladi, Andrews, Gordon bijection ⋮ Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities

Cites Work

• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities
• Lattice gas generalization of the hard hexagon model. III: \(q\)-trinomial coefficients
• A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities
• Elements of the annihilating ideal of a standard module
• On some representations of twisted affine Lie algebras and combinatorial identities
• On a partition theorem of Göllnitz and quartic transformations
• Generalizations of Schur's partition theorem
• A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type
• Unnamed Item

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