A Trinomial Analogue of Bailey's Lemma and N=2 Superconformal Invariance

We propose and prove a trinomial version of the celebrated Bailey's lemma. As an application we obtain new fermionic representations for characters of some unitary as well as nonunitary models of N = 2 superconformal field theory (SCFT). We also establish interesting relations between N = 1 and N = 2 models of SCFT with central charges $(3/2)( 1 -{2(2 - 4\nu)^2}/{2(4\nu)})$ and $3(1 - 2/{4\nu})$. A number of new mock theta function identities are derived.Comment: Reference and note adde

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Bailey flows and Bose-Fermi identities for the conformal coset models (A1(1))N×(A1(1))N′/(A1(1))N+N′(A^{(1)}_1)_N\times (A^{(1)}_1)_{N'}/(A^{(1)}_1)_{N+N'}

We use the recently established higher-level Bailey lemma and Bose-Fermi polynomial identities for the minimal models $M(p,p')$ to demonstrate the existence of a Bailey flow from $M(p,p')$ to the coset models $(A^{(1)}_1)_N\times (A^{(1)}_1)_{N'}/(A^{(1)}_1)_{N+N'}$ where $N$ is a positive integer and $N'$ is fractional, and to obtain Bose-Fermi identities for these models. The fermionic side of these identities is expressed in terms of the fractional-level Cartan matrix introduced in the study of $M(p,p')$. Relations between Bailey and renormalization group flow are discussed.Comment: 28 pages, AMS-Latex, two references adde