Cylindric partitions, q-difference equations and Rogers-Ramanujan type identities

Abstract: Cylindric partitions, which were introduced by Gessel and Krattenthaler in 1997, can be seen as generalisations of integer partitions involving periodicity conditions. Since the 1980s and the founding work of Lepowsky and Wilson on Rogers-Ramanujan identities, several connections between characters of Lie algebras and partition identities have emerged. In particular, Andrews, Schilling and Warnaar discovered in 1998 a family of partition identities related to characters of A_2. Recently, Corteel and Welsh established a q-difference equation satisfied by generating functions for cylindric partitions and used it to reprove the A_2 Rogers-Ramanujan identities of Andrews, Schilling and Warnaar. We build on this technique to discover and prove a new family of A_2 Rogers-Ramanujan identities and give explicitly positive expressions for certain characters. This is joint work with Sylvie Corteel and Ali Uncu.

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11