Abstract:Kostant's partition function counts the number of distinct ways to express a weight of a classical Lie algebra g as a sum of positive roots of g. We refer to each of these expressions as decompositions of a weight. Our main result considers an infinite family of weights, irrespective of Lie type, for which we establish a closed formula for the q-analog of Kostant's partition function and then prove that the (normalized) distribution of the number of positive roots in the decomposition of any of these weights c… Show more
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