Coding the principal character formula for affine Kac-Moody lie algebras

DOI10.1090/S0025-5718-03-01577-1zbMath1023.17016OpenAlexW2083000382MaRDI QIDQ4417174

Maegan K. Bos

Publication date: 28 July 2003

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-03-01577-1

zbMATH Keywords

principal character for affine Lie algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (9)

On \(q\)-series for principal characters of standard \(A_2^{( 2 )}\)-modules ⋮ The butterfly sequence: the second difference sequence of the numbers of integer partitions with distinct parts ⋮ Principal subspaces of basic modules for twisted affine Lie algebras, \(q\)-series multisums, and Nandi's identities ⋮ Proofs and reductions of various conjectured partition identities of Kanade and Russell ⋮ Adjoint Orbits of Semi-Simple Lie Groups and Lagrangian Submanifolds ⋮ Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type ⋮ Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities ⋮ Andrews-Gordon type series for the level 5 and 7 standard modules of the affine Lie algebra $A^{(2)}_2$ ⋮ New partition identities from \(C^{(1)}_\ell\)-modules

Uses Software

• Maple

Cites Work

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• Structure of certain standard modules for \(A_ n^{(1)}\) and the Rogers-Ramanujan identities
• Structure of some standard modules for \(C_ n^{(1)}\)
• 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
• A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities
• On some representations of twisted affine Lie algebras and combinatorial identities
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• Structure of the level two Standard Modules for the affine Lie algebra
• Structure of the level one standard modules for the affine Lie algebras 𝐵_{𝑙}⁽¹⁾,𝐹⁽¹⁾₄ and 𝐺⁽¹⁾₂
• Level two representations of and Rogers-Ramanujan identities

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