# Pamela Harris: Recent results on Kostant’s partition function

**Time: **
Tue 2020-02-11 10.00 - 10.50

**Lecturer: **
Pamela Harris, Williams College

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan

### Abstract

In this talk we introduce Kostant’s partition function which counts the number of ways to represent a particular weight (vector) as a nonnegative integral sum of positive roots of a Lie algebra. We provide two fundamental uses for this function. The first is associated with the computation of weight multiplicities in finite-dimensional irreducible representations of classical Lie algebras, and the second is in the computation of volumes of flow polytopes. We provide some recent results in the representation theory setting, and state a direction of ongoing research related to the computation of the volume of a flow polytopes associated to a Caracol diagram.