Demystifying a divisibility property of the Kostant partition function

Karola Mészáros

Vol. 260 (2012), No. 1, 215–225

DOI: 10.2140/pjm.2012.260.215

Abstract

We prove a family of identities connected to a divisibility property of the Kostant partition function. A special case of these identities first appeared in a paper of Baldoni and Vergne. To prove their identities, Baldoni and Vergne used residue techniques, and called the resulting divisibility property “mysterious.” Our proofs are entirely combinatorial and provide a natural explanation for why divisibility occurs, both in the Baldoni and Vergne identities and in their generalizations.

Keywords

Kostant partition function, divisibility, flow

Mathematical Subject Classification 2010

Primary: 05E10

Milestones

Received: 27 November 2011

Revised: 4 April 2012

Accepted: 9 July 2012

Published: 11 October 2012