The t-analog of the basic string function for twisted affine Kac–Moody algebras

We study Lusztigʼs t-analog of weight multiplicities associated to level one representations of twisted affine Kac–Moody algebras. An explicit closed form expression is obtained for the corresponding t-string function using constant term identities of Macdonald and Cherednik. The closed form involves the generalized exponents of the graded pieces of the twisted affine algebra, considered as modules for the underlying finite dimensional simple Lie algebra. This extends previous work on level 1 t-string functions for the untwisted simply-laced affine Kac–Moody algebras.