Specialized characters of affine superalgebras
type: Item
instance of: scholarly article
title: Specialized characters of affine superalgebras
zbMATH Open document ID: 0927.17016
author: George Golitzin
published in: Journal of Algebra
publication date: 1999-12-15T00:00:00Z
review text: Let \({\mathfrak g}(A)\) be the super analogue of the Kac-Moody algebra with symmetrizable Cartan matrix \(A\). In [\textit{V. G. Kac}, Adv. Math. 30, 85-136 (1978; Zbl 0391.17010)] a super version of the Weyl-Kac character formula for irreducible highest weight modules enables to compute the principal specialization of such characters. This specialization corresponds to the principal gradation of \({\mathfrak g}(A)\) in which simple root vectors are of first degree. In the paper of Kac this formula was given only for the non-super case. The purpose of the paper under review is to establish the appropriate super version when the principal gradation of \({\mathfrak g}(A)\) assigns degree 1 to the odd simple roots and degree 2 to the even ones. Then the author computes the specialized characters of the fundamental highest weight modules of the affine superalgebras of rank 1, namely \(A^{(2)}(0,1)\cong C^{(2)}(2)\), \(B^{(1)}(0,1)\) and \(A^{(4)}(0,2)\). Finally, the author gives the characters of the representations of the superalgebras \(A^{(4)}(0,2l)\) and \(A^{(2)}(0,2l-1)\) described in his earlier paper [\textit{G. Golitzin}, J. Algebra 117, No. 1, 198-226 (1988; Zbl 0652.17013)].
Mathematics Subject Classification ID: 17B67
Mathematics Subject Classification ID: 17B69
zbMATH DE Number: 1271652
zbMATH Keywords: affine Lie superalgebras
zbMATH Keywords: representations of Lie superalgebras
zbMATH Keywords: specialized characters
zbMATH Keywords: highest weight modules
reviewed by: Vesselin Drensky
MaRDI profile type: Publication
full work available at URL: jabr.1996.6537
OpenAlex ID: W2073119311
cites work: Representation of the affine superalgebras \(A^{(4)}(0,2\ell)\), \(A^{(2)}(0,2\ell -1)\) and their subalgebras \(A_{2\ell}^{(2)}\), \(A^{(2)}_{2\ell -1}\) by vertex operators
cites work: Basic representation of the affine superalgebra \(A^{(2)}(0,1)\)
cites work: Lie superalgebras
cites work: Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
cites work: Lie algebraic approaches to classical partition identities
cites work: The structure of standard modules. I: Universal algebras and the Rogers- Ramanujan identities
cites work: Affine root systems and Dedekind's \(\eta\)-function
DOI: 10.1006/JABR.1996.6537
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description: scientific article; zbMATH DE number 1271652