Asymptotic formulas for coefficients of Kac-Wakimoto Characters

作者：Bringmann Kathrin^*; Mahlburg Karl

来源：Mathematical Proceedings of the Cambridge Philosophical Society, 2013, 155(1): 51-72.

DOI：10.1017/S0305004112000680

We study the coefficients of Kac and Wakimoto%26apos;s character formulas for the affine Lie superalgebras sl( n + 1 vertical bar 1)(boolean AND). 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%26apos;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.

• 出版日期2013-7