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Pré-Publication, Document De Travail Année : 2022

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

Roberto Bramati
Angela Pasquale
Tomasz Przebinda
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Résumé

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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Dates et versions

hal-03744457 , version 1 (02-08-2022)
hal-03744457 , version 2 (23-08-2022)
hal-03744457 , version 3 (18-10-2022)

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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-03744457v1⟩
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