Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 259-281.

LOGARITHMIC VERTEX ALGEBRAS RELATED TO sp(4)

Dražen Adamović and Antun Milas

Department of Mathematics, Faculty of Science, University of Zagreb, 10 000 Zagreb, Croatia
e-mail: adamovic@math.hr

Department of Mathematics and Statistics, SUNY-Albany, Albany NY 12222, USA
e-mail: amilas@albany.edu

Abstract.   We present several results and conjectures pertaining to parafermion vertex algebra and related logarithmic vertex algebras. Starting from the tensor product of two copies of the singlet vertex algebra M(2), we consider various subalgebras that appear in its decomposition including N-1(sl(2)) and its Z2-fixed point algebra, and the S2-symmetric orbifold of the singlet vertex algebra M(2). In particular, we show that N-1(sl(2)) has an extension to a W-algebra of type (2, 3, 4, 5, 6, 7, 8). Finally we state some conjectures about singlet and triplet type W-algebras of type sp(4) and their characters.

2020 Mathematics Subject Classification.   17B69, 17B20, 17B67.

Key words and phrases.   Vertex algebra, parafermion algebra.

Full text (PDF) (free access)

DOI: https://doi.org/10.21857/94kl4c1j8m

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