Structure of certain standard modules for \(A_ n^{(1)}\) and the Rogers-Ramanujan identities

DOI10.1016/0021-8693(84)90098-XzbMath0536.17008MaRDI QIDQ791623

Kailash C. Misra

Publication date: 1984

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

zbMATH Keywords

Rogers-Ramanujan identitiesaffine Lie algebraKac-Moody Lie algebrasconcrete realizationsgraded heighest weight modulesprincipal Heisenberg subalgebrastandard modules of level twoZ-algebras

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Infinite-dimensional Lie (super)algebras (17B65) Elementary theory of partitions (11P81)

Related Items (16)

Vertex operator representations for toroidal lie algebra of typeB_l ⋮ ON MULTI-COLOR PARTITIONS AND THE GENERALIZED ROGERS–RAMANUJAN IDENTITIES ⋮ Structure of some nonstandard modules for \(C_ n^{(1)}\) ⋮ Level one standard modules for affine symplectic Lie algebras ⋮ Level two representations of and Rogers-Ramanujan identities ⋮ Structure of the level two Standard Modules for the affine Lie algebra ⋮ Leading terms of relations for standard modules of the affine Lie algebras \(C_n^{(1)}\) ⋮ Structure of the level two standard modules for the affine lie algebra D⁽³⁾₄ ⋮ A Construction of the Level 3 Modules for the Affine Lie Algebra 𝐴₂⁽²⁾ and a New Combinatorial Identity of the Rogers-Ramanujan Type ⋮ Elements of the annihilating ideal of a standard module ⋮ Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz-Gordon identities ⋮ Coding the principal character formula for affine Kac-Moody lie algebras ⋮ Level two standard \(\tilde A_ n\)-modules ⋮ Principal subspaces for the affine Lie algebras in types \(D, E\) and \(F\) ⋮ Structure of some standard modules for \(C_ n^{(1)}\) ⋮ The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities

Cites Work

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• The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
• Realization of the basic representations of the Euclidean Lie algebras
• Two constructions of affine Lie algebra representations and boson-fermion correspondence in quantum field theory
• A Lie theoretic interpretation and proof of the Rogers-Ramanujan identities
• Basic representations of affine Lie algebras and dual resonance models
• Unitary representations of some infinite dimensional groups
• Infinite-dimensional Lie algebras and Dedekind's \(\eta\)-function
• Lie algebraic approaches to classical partition identities
• Macdonald-type identities
• Construction of the affine Lie algebra \(A^{(1)}_1\)
• The Weyl-Kac character formula and power series identities
• A new class of Lie algebras
• The Rogers-Ramanujan identities: Lie theoretic interpretation and proof
• A new family of algebras underlying the Rogers-Ramanujan identities and generalizations
• MacDonald Identities and Euclidean Lie Algebras
• On the Geometry of Numbers in Elementary Number Theory
• Euclidean Lie Algebras
• SIMPLE IRREDUCIBLE GRADED LIE ALGEBRAS OF FINITE GROWTH

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