The t-analogs of string functions for A₁⁽¹⁾ and Hecke indefinite modular forms

2013/02/25 by Sachin S. Sharma, Sharma, Sachin S., Sankaran Viswanath +1
Mathematics · #17B67 #33B67 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:17B67 #msc:33B67

paper · pdf · doi:10.48550/arxiv.1302.6200

Revised version

arxiv created 2015/07/23 · arxiv updated 2015/07/24

Abstract

We study generating functions for Lusztig's t-analog of weight multiplicities associated to integrable highest weight representations of the simplest affine Lie algebra A₁⁽¹⁾. At t=1, these reduce to the \em string functions of A₁⁽¹⁾, which were shown by Kac and Peterson to be related to certain Hecke indefinite modular forms. Using their methods, we obtain a description of the general t-string function; we show that its values can be realized as radial averages of a certain extension of the Hecke indefinite modular form.

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