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

Abstract : Let (G,G') be a reductive dual pair in Sp(W) with rank G ≤ rank G' and G' semisimple. The image of the Casimir element of the universal enveloping algebra of G' under the Weil representation ω is a Capelli operator. It is a hermitian operator acting on the smooth vectors of the representation space of ω. We compute the resonances of a natural multiple of a translation of this operator for small split orthosymplectic dual pairs. The corresponding resonance representations turn out to be GG'-modules in Howe's correspondence. We determine them explicitly.
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https://hal.archives-ouvertes.fr/hal-03744457
Contributor : Bramati Roberto Connect in order to contact the contributor
Submitted on : Tuesday, August 2, 2022 - 10:28:45 PM
Last modification on : Thursday, August 4, 2022 - 3:23:02 AM

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  • HAL Id : hal-03744457, version 1

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Roberto Bramati, Angela Pasquale, Tomasz Przebinda. The resonances of the Capelli operators for small split orthosymplectic dual pairs. 2022. ⟨hal-03744457⟩

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