A BASIS OF THE BASIC $\mathfrak{sl} ({\bf 3}, {\mathbb C})^~$-MODULE

DOI10.1142/S0219199701000512zbMath1004.17003arXivmath/9812029OpenAlexW1864760197MaRDI QIDQ4539766

Mirko Primc, Arne Meurman

Publication date: 10 July 2002

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9812029

zbMATH Keywords

Rogers-Ramanujan identitiesvertex operators

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Vertex operators; vertex operator algebras and related structures (17B69)

Related Items (13)

Multi-grounded partitions and character formulas ⋮ On series expansions of Capparelli's infinite product ⋮ A RECURRENCE RELATION FOR CHARACTERS OF HIGHEST WEIGHT INTEGRABLE MODULES FOR AFFINE LIE ALGEBRAS ⋮ IdentityFinder and Some New Identities of Rogers–Ramanujan Type ⋮ On a Koszul complex related to the principal subspace of the basic vacuum module for \(A_1^{(1)}\) ⋮ Generalisations of Capparelli's and Primc's identities. I: Coloured Frobenius partitions and combinatorial proofs ⋮ On a Rogers-Ramanujan type identity from crystal base theory ⋮ Leading terms of relations for standard modules of the affine Lie algebras \(C_n^{(1)}\) ⋮ Combinatorial relations among relations for level 2 standard Cn(1)-modules ⋮ Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities ⋮ On partition identities of Capparelli and Primc ⋮ Combinatorial bases of basic modules for affine Lie algebras Cn(1) ⋮ False theta functions and companions to Capparelli's identities

Cites Work

• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• The structure of standard modules. II: The case \(A_ 1^{(1)}\), principal gradation
• Annihilating ideals of standard modules of \({\mathfrak sl}(2,{\mathbb{C}})^\sim\) and combinatorial identities
• Level one standard modules for affine symplectic Lie algebras
• Application of the numerator formula to k-rowed plane partitions
• Refinements and generalizations of Capparelli's conjecture on partitions
• A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type

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