A conjecture of Warnaar-Zudilin from deformations of lie superalgebras

Source abstract

Abstract We prove a collection of q -series identities conjectured by Warnaar and Zudilin and appearing in recent work with H. Kim in the context of superconformal field theory. Our proof utilizes a deformation of the simple affine vertex operator superalgebra $$L_k(\mathfrak {osp}_{1|2n})$$ L k ( osp 1 | 2 n ) into the principal subsuperspace of $$L_k({\mathfrak {s}}{\mathfrak {l}}_{1|2n+1})$$ L k ( s l 1 | 2 n + 1 ) in a manner analogous to earlier work of Feigin-Stoyanovsky. This result fills a gap left by Stoyanovsky, showing that for all positive integers N , k the character of the principal subspace of type $$A_N$$ A N at level k can be identified with the (super)character of a simple affine vertex operator (super)algebra at the same level.