A conjecture of Warnaar-Zudilin from deformations of lie superalgebras

Creutzig T, Garner N (2026)

Publication Type: Journal article

Publication year: 2026

Journal

Research in the Mathematical Sciences Springer

Book Volume: 13

Article Number: 33

Journal Issue: 2

DOI: 10.1007/s40687-026-00613-2

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 Lk(osp1|2n) into the principal subsuperspace of Lk(sl1|2n+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 AN at level k can be identified with the (super)character of a simple affine vertex operator (super)algebra at the same level.

Authors with CRIS profile

Thomas Creutzig Lehrstuhl für Darstellungstheorie

Involved external institutions

University of Oxford

United Kingdom (GB)

How to cite

APA:

Creutzig, T., & Garner, N. (2026). A conjecture of Warnaar-Zudilin from deformations of lie superalgebras. Research in the Mathematical Sciences, 13(2). https://doi.org/10.1007/s40687-026-00613-2

MLA:

Creutzig, Thomas, and Niklas Garner. "A conjecture of Warnaar-Zudilin from deformations of lie superalgebras." Research in the Mathematical Sciences 13.2 (2026).

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