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Tuesday, 15.12.2020 | 14.15 - 15.45 Uhr

Oberseminar Geometrische Analysis und Zahlentheorie (online): Jan Frahm (Aarhus University)

Conformally invariant differential operators on Heisenberg groups and minimal representations

Abstract: On Euclidean space, the Fourier transform intertwines partial derivatives and coordinate multiplications. As a consequence, solutions to a constant coefficient PDE $p(D)u=0$ are mapped to distributions supported on the variety $\{p(x)=0\}$. In the context of unitary representation theory of semisimple Lie groups, so-called minimal representations are often realized on Hilbert spaces of solutions to systems of constant coefficient PDEs whose inner product is difficult to describe (the non-compact picture of a degenerate principal series). The Euclidean Fourier transform provides a new realization on a space of distributions supported on a variety where the invariant inner product is simply an $L^2$-inner product on the variety. Recently, similar systems of differential operators have been constructed on Heisenberg groups. In this talk I will explain how to use the Heisenberg group Fourier transform to obtain a similar picture in this context.

Bei Interesse an einer Teilnahme bitten wir vorab mit Tobias Weich per Mail Kontakt aufzunehmen, damit der Teilnahmelink geteilt werden kann.

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