The Rogers-Ramanujan recursion and intertwining operators

S. Capparelli; J. Lepowsky; A. Milas

doi:10.1142/S0219199703001191

The Rogers-Ramanujan recursion and intertwining operators

S. Capparelli, J. Lepowsky, A. Milas

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

We use vertex operator algebras and intertwining operators to study certain substructures of standard A₁⁽¹⁾ -modules, allowing us to conceptually obtain the classical Rogers-Ramanujan recursion. As a consequence we recover Feigin-Stoyanovsky's character formulas for the principal subspaces of the level 1 standard A₁⁽¹⁾-modules.

Original language	English (US)
Pages (from-to)	947-966
Number of pages	20
Journal	Communications in Contemporary Mathematics
Volume	5
Issue number	6
DOIs	https://doi.org/10.1142/S0219199703001191
State	Published - Dec 2003

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Affine Lie algebras
Partitions
Vertex operator algebras
Vertex operators

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10.1142/S0219199703001191

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abstract = "We use vertex operator algebras and intertwining operators to study certain substructures of standard A1(1) -modules, allowing us to conceptually obtain the classical Rogers-Ramanujan recursion. As a consequence we recover Feigin-Stoyanovsky's character formulas for the principal subspaces of the level 1 standard A1(1)-modules.",

keywords = "Affine Lie algebras, Partitions, Vertex operator algebras, Vertex operators",

author = "S. Capparelli and J. Lepowsky and A. Milas",

note = "Funding Information: The first author gratefully acknowledges the partial support of MIUR (Ministero dell{\textquoteright}Istruzione, dell{\textquoteright}Universit{\`a} e della Ricerca). The second and third authors gratefully acknowledge partial support from NSF grant DMS-0070800.",

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AU - Capparelli, S.

AU - Lepowsky, J.

AU - Milas, A.

N1 - Funding Information: The first author gratefully acknowledges the partial support of MIUR (Ministero dell’Istruzione, dell’Università e della Ricerca). The second and third authors gratefully acknowledge partial support from NSF grant DMS-0070800.

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N2 - We use vertex operator algebras and intertwining operators to study certain substructures of standard A1(1) -modules, allowing us to conceptually obtain the classical Rogers-Ramanujan recursion. As a consequence we recover Feigin-Stoyanovsky's character formulas for the principal subspaces of the level 1 standard A1(1)-modules.

AB - We use vertex operator algebras and intertwining operators to study certain substructures of standard A1(1) -modules, allowing us to conceptually obtain the classical Rogers-Ramanujan recursion. As a consequence we recover Feigin-Stoyanovsky's character formulas for the principal subspaces of the level 1 standard A1(1)-modules.

KW - Affine Lie algebras

KW - Partitions

KW - Vertex operator algebras

KW - Vertex operators

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ER -

The Rogers-Ramanujan recursion and intertwining operators

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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