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

Abstract

Kostant's partition function counts the number of ways to represent a particular vector (weight) as a nonnegative integral sum of positive roots of a Lie algebra. For a given weight the $q$-analog of Kostant's partition function is a polynomial where the coefficient of $q^k$ 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 $D$.

21 pages, includes new closed formulas

References in corpus (2)

• Flow polytopes of signed graphs and the Kostant partition function
• Generating functions and multiplicity formulas: the case of rank two simple Lie algebras

Cited by in corpus (1)

• On the poset and asymptotics of Tesler Matrices