A Character Formula for the Category \~O

Abstract

One may construct, for any function on the integers, an irreducible module of level zero for affine sl(2), using the values of the function as structure constants. The modules constructed using exponential-polynomial functions realise the irreducible modules with finite-dimensional weight spaces in the category \~O of Chari. In this work, an expression for the formal character of such a module is derived using the highest-weight theory of truncations of the loop algebra.