Rad HAZU, Matematičke znanosti, Vol. 21 (2017), 75-87.

A NOTE ON THE AFFINE VERTEX ALGEBRA ASSOCIATED TO gl(1|1) AT THE CRITICAL LEVEL AND ITS GENERALIZATIONS

Dražen Adamović

Department of Mathematics, Faculty of Science, University of Zagreb, 10000 Zagreb, Croatia
e-mail: adamovic@math.hr


Abstract.   In this note we present an explicit realization of the affine vertex algebra Vcri(gl(1|1)) inside of the tensor product FM where F is a fermionic verex algebra and M is a commutative vertex algebra. This immediately gives an alternative description of the center of Vcri(gl(1|1)) as a subalgebra M0 of M. We reconstruct the Molev-Mukhin formula for the Hilbert-Poincare series of the center of Vcri(gl(1|1)). Moreover, we construct a family of irreducible Vcri(gl(1|1))-modules realized on F and parameterized by χ+, χ-C((z)). We propose a generalization of Vcri(gl(1|1)) as a critical level version of the super W1+∞ vertex algebra.

2010 Mathematics Subject Classification.   17B69, 17B67.

Key words and phrases.   Vertex algebras, affine Lie superalgebras, critical level, W-algebras.


Full text (PDF) (free access)

DOI: http://doi.org/10.21857/yrvgqtpk89


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