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.

MSC:

 05A19 Combinatorial identities, bijective combinatorics 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 11P82 Analytic theory of partitions 05A30 $$q$$-calculus and related topics
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