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Tomasz Przebinda

Publications and source records attributed to Tomasz Przebinda.

5 recordsLinked to original sources
arXiv2024

The big theta

We show that Howe's big quotient is obtained via the tensoring over appropriate algebra.

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arXiv2023

The character correspondence in the stable range over a p-adic field

Given a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. If the pair is in the stable range and if the representation is unitary, then the resulting distribution is the character of the representation obtained via Howe's correspondence. This construction was transferred to the p-adic case and a conjecture was formulated. In this note we verify a weaker version of this conjecture for dual pairs in the stable range over a p-adic field.

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arXiv2023

A Cauchy--Harish-Chandra integral for a dual pair over a p-adic field, the definition and a conjecture

For a real irreducible dual pair there is an integral kernel operator which maps the distribution character of an irreducible admissible representation of the group with the smaller or equal rank to an invariant eigendistribution on the group with the larger or equal rank. The purpose of this article is to transfer this construction to the p-adic case. We provide the precise definition of the integral kernel operator and formulate a conjecture.

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arXiv2022

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

Let $(G,G')$ be a reductive dual pair in $Sp(W)$ with rank $G\leq$ 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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