On Some Theorems of Hirschhorn

Abstract

It is found that four theorems of Hirschhorn [Hirschhorn, M. D. (1979). Some partition theorems of the Rogers–Ramanujan type. J. Comb. Th. A 27:33–37] correspond to standard representations of an affine Lie algebra. Using this correspondence two more theorems of the same type are found. It turns out that a classical result of Euler also appears in this context.

Key Words:

• Partition identities
• Lie algebras

Acknowledgment

S.C. gratefully acknowledges the partial support of MIUR (Ministero dell'Istruzione, dell'Università e della Ricerca).

Notes

^#Communicated by K. Misra.