Joseph-like ideals and harmonic analysis for osp(m|2n)

Understand

The Joseph ideal in the universal enveloping algebra U(so(m)) is the annihilator ideal of the so(m)-representation on the harmonic functions on R^{m-2}.

• The Joseph ideal for sp(2n) is the annihilator ideal of the Segal-Shale-Weil (metaplectic) representation.
• Both ideals can be constructed in a unified way from a quadratic relation in the tensor algebra of g for g equal to so(m) or sp(2n).
• In this paper we construct two analogous ideals in the tensor algebra of g and U(g) for g the orthosymplectic Lie superalgebra osp(m|2n)=spo(2n|m) and prove that they have unique characterizations that naturally extend the classical case.