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Asymptotic formulas for coefficients of Kac–Wakimoto Characters

Published online by Cambridge University Press:  22 February 2013

KATHRIN BRINGMANN  and
KARL MAHLBURG
KATHRIN BRINGMANN
Affiliation:
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany. e-mail: [email protected]
KARL MAHLBURG
Affiliation:
Department of Mathematics, Princeton University, NJ 08544, U.S.A. e-mail: [email protected] Department of Mathematics, Louisiana State University, LA 70803, U.S.A. e-mail: [email protected]
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Abstract

We study the coefficients of Kac and Wakimoto's character formulas for the affine Lie superalgebras sℓ(n+1|1)∧. The coefficients of these characters are the weight multiplicities of irreducible modules of the Lie superalgebras, and their asymptotic study begins with Kac and Peterson's earlier use of modular forms to understand the coefficients of characters for affine Lie algebras. In the affine Lie superalgebra setting, the characters are products of weakly holomorphic modular forms and Appell-type sums, which have recently been studied using developments in the theory of mock modular forms and harmonic Maass forms. Using our previously developed extension of the Circle Method for products of mock modular forms along with the Saddle Point Method, we find asymptotic series expansions for the coefficients of the characters with polynomial error.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 1 , July 2013 , pp. 51 - 72
Copyright
Copyright © Cambridge Philosophical Society 2013 

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