Invariant differential operators on a class of multiplicity free spaces

Hubert Rubenthaler (1)

1 IRMA - Institut de Recherche Mathématique Avancée

If $(G,V)$ is a multiplicity 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.

Mots clés: invariant differential operators; multiplicity free spaces; Smith algebras; radial components

Domaines: Théorie des représentations [math.RT]; Anneaux et algèbres [math.RA]

Hubert Rubenthaler. Invariant differential operators on a class of multiplicity free spaces. Pacific Journal of Mathematics, 2014, 270 (2), pp.473-510. ⟨10.2140/pjm.2014.270.473⟩. ⟨hal-00574585v2⟩