The resonances of the Capelli operators for small split orthosymplectic dual pairs

Roberto Bramati, Angela Pasquale, Tomasz Przebinda

Let $(G,G^{\prime })$ be a reductive dual pair in $Sp(W)$ with rank $G\le$ rank $G^{\prime }$ and $G^{\prime }$ semisimple. The image of the Casimir element of the universal enveloping algebra of $G^{\prime }$ under…