The Rogers-Selberg recursions, the Gordon-Andrews identities and intertwining operators

被引：53

作者：

Capparelli, S.

Lepowsky, J. ^{[1
]}

Milas, A.

机构：

[1] Rutgers State Univ, Dept Math, Piscataway, NJ 08854 USA

[2] Univ Arizona, Dept Math, Tucson, AZ 85721 USA

[3] Univ Roma La Sapienza, Dipartimento Me Mo Mat, I-00161 Rome, Italy

来源：

RAMANUJAN JOURNAL | 2006年 / 12卷 / 03期

基金：

美国国家科学基金会;

关键词：

affine Lie algebras; difference equations; vertex operator algebras;

D O I：

10.1007/s11139-006-0150-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using the theory of intertwining operators for vertex operator algebras we show that the graded dimensions of the principal subspaces associated to the standard modules for sl(2) satisfy certain classical recursion formulas of Rogers and Selberg. These recursions were exploited by Andrews in connection with Gordon's generalization of the Rogers-Ramanujan identities and with Andrews' related identities. The present work generalizes the authors' previous work on intertwining operators and the Rogers-Ramanujan recursion.

引用

页码：379 / 397

页数：19

共 39 条

[1]

Andrews G. E., 1976, ENCY MATH ITS APPL, V2

[2]

Andrews G.E., 1967, J COMB THEORY, V2, P431

[3] AN ANALYTIC PROOF OF ROGERS-RAMANUJAN-GORDON IDENTITIES [J].