×

The Rogers-Ramanujan recursion and intertwining operators. (English) Zbl 1039.05005

Summary: We use vertex operator algebras and intertwining operators to study certain substructures of standard \(A_1^{(1)}\)-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 \(A_1^{(1)}\)-modules.

MSC:

05A17 Combinatorial aspects of partitions of integers
17B69 Vertex operators; vertex operator algebras and related structures
05A19 Combinatorial identities, bijective combinatorics
11P81 Elementary theory of partitions
33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Andrews G., The Theory of Partitions 2, in: Encyclopedia of Mathematics and Its Applications (1976) · Zbl 0371.10001
[2] DOI: 10.1073/pnas.83.10.3068 · Zbl 0613.17012 · doi:10.1073/pnas.83.10.3068
[3] Capparelli S., Ramanujan J.
[4] Dong C., Generalized Vertex Algebras and Relative Vertex Operators 112, in: Progress in Mathematics (1993) · Zbl 0803.17009
[5] Frenkel I. B., Mem. Amer. Math. Soc. 104
[6] DOI: 10.1007/BF01391662 · Zbl 0493.17010 · doi:10.1007/BF01391662
[7] Frenkel I. B., Vertex Operator Algebras and the Monster 134, in: Pure and Appl. Math. (1988) · Zbl 0674.17001
[8] DOI: 10.1016/0022-4049(95)00143-3 · Zbl 0871.17018 · doi:10.1016/0022-4049(95)00143-3
[9] DOI: 10.1017/CBO9780511626234 · doi:10.1017/CBO9780511626234
[10] DOI: 10.1016/0001-8708(78)90004-X · Zbl 0384.10008 · doi:10.1016/0001-8708(78)90004-X
[11] Lepowsky J., Structure of the Standard Modules for the Affine Lie Algebra A1(1) 46, in: Contemporary Mathematics (1985) · Zbl 0569.17007
[12] DOI: 10.1007/BF01940329 · Zbl 0388.17006 · doi:10.1007/BF01940329
[13] DOI: 10.1073/pnas.78.12.7254 · Zbl 0472.17005 · doi:10.1073/pnas.78.12.7254
[14] DOI: 10.1007/BF01388447 · Zbl 0577.17009 · doi:10.1007/BF01388447
[15] Meurman A., Mem. Amer. Math. Soc. 137
[16] Rogers L. J., Proc. Camb. Phil. Soc. 19 pp 211–
[17] DOI: 10.1007/BF01208274 · Zbl 0495.22017 · doi:10.1007/BF01208274
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.