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A trinomial analogue of Bailey’s lemma and $N=2$ superconformal invariance. (English) Zbl 0906.05004
Summary: 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 ${3\over 2}\left(1-{2(2-4\nu)^2\over 2(4\nu)}\right)$ and $3\left(1- {2\over 4\nu}\right)$. A number of new mock theta function identities are derived.

05A19Combinatorial identities, bijective combinatorics
81T40Two-dimensional field theories, conformal field theories, etc.
11P82Analytic theory of partitions
05A30$q$-calculus and related topics
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