The q-analog of Kostant's partition function and the highest root of the simple Lie algebras

For a given weight of a complex simple Lie algebra, the q-analog of Kostant’s partition function is a polynomial valued function in the variable q, where the coefficient of q is the number of ways the weight can be written as a nonnegative integral sum of exactly k positive roots. In this paper we determine generating functions for the q-analog of Kostant’s partition function when the weight in question is the highest root of the classical Lie algebras of types B, C, and D, and the exceptional Lie algebras of type G2, F4, E6, E7, and E8. ∗ This research was supported by research funds from Harvey Mudd College. P.E. HARRIS ET AL. /AUSTRALAS. J. COMBIN. 71 (1) (2018), 68–91 69

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