No abstract

Given a simple Lie algebra g, Kostant's weight q-multiplicity formula is an alternating sum over the Weyl group whose terms involve the q-analog of Kostant's partition function. For ξ (a weight of g), the q-analog of Kostant's partition function is a polynomial-valued function defined by ℘q(ξ) = ciq i where ci is the number of ways ξ can be written as a sum of i positive roots of g. In this way, the evaluation of Kostant's weight q-multiplicity formula at q = 1 recovers the multiplicity of a weight in a highest weight representation of g. In this paper, we give closed formulas for computing weight q-multiplicities in a highest weight representation of the exceptional Lie algebra g2.