Invariant differential operators on a class of multiplicity-free spaces

Hubert Rubenthaler

Vol. 270 (2014), No. 2, 473–510

DOI: 10.2140/pjm.2014.270.473

Abstract

If $\left(G,V\right)$ is a multiplicity-free space with a one-dimensional quotient, we give generators and relations for the noncommutative algebra $D{\left(V\right)}^{G^{\prime }}$ of invariant differential operators under the semisimple part $G^{\prime }$ of the reductive group $G$. More precisely we show that $D{\left(V\right)}^{G^{\prime }}$ is the quotient of a Smith algebra by a completely described two-sided ideal.

Keywords

multiplicity-free space, invariant differential operator, Smith algebra

Mathematical Subject Classification 2010

Primary: 22E46, 16S32

Secondary: 11S90

Milestones

Received: 26 March 2013

Revised: 8 January 2014

Accepted: 27 January 2014

Published: 22 August 2014