Alladi Ramakrishnan Hall

The t-analogue of string functions for the affine Kac-Moody algebras.

Sachin Sharma

IMSc and HRI.

We study Lusztig’s t-analogue of weight multiplicities associated to the irreducible integrable highest weight modules of affine Kac-Moody algebras. First, for the level one represen-
tation of twisted affine Kac-Moody algebras, we obtain an explicit closed form expression for the corresponding t-string function using constant term identities of Macdonald and Cherednik. The closed form involves the generalised exponents of the graded pieces of the twisted
affine algebra, considered as modules for the underlying finite dimensional simple Lie algebra. Next, for affine sl2, we give a basis for the weight spaces of its basic representation, which is compatible with the affine Brylinski-Kostant filtration. Using this basis we give an alternative derivation of the expression for the t-string
function of the basic representation.