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Invariant differential operators on a class of multiplicity free spaces (1103.1721v2)
Published 9 Mar 2011 in math.RT and math.RA
Abstract: If $(G,V)$ is a multiplity free space with a one dimensional quotient we give generators and relations for the non-commutative algebra $D(V){G'}$ of invariant differential operators under the semi-simple part $G'$ of the reductive group $G$. More precisely we show that $D(V){G'}$ is the quotient of a Smith algebra by a completely described two-sided ideal.