Every irreducible unitary representation of the Heisenberg group over a local field is c-tempered with a common Følner sequence, yielding asymptotic Schur orthogonality and convergence to the braiding operator.
On Kazhdan-Yom Din asymptotic Schur orthogonality for K-finite matrix coefficients
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abstract
In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an asymptotic form of Schur's orthogonality for tempered irreducible unitary representations of semisimple groups defined over local fields. In the non-Archimedean case, they established such an orthogonality for $K$-finite matrix coefficients. Building on their work, and exploiting the admissibility of irreducible unitary representations, we prove the analogous result in the Archimedean case.
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Asymptotic Schur orthogonality relations for Heisenberg groups over local fields
Every irreducible unitary representation of the Heisenberg group over a local field is c-tempered with a common Følner sequence, yielding asymptotic Schur orthogonality and convergence to the braiding operator.