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Montag, 14.05.2018 | 16.45 - 17.45 Uhr | Hörsaal D2

Mathematisches Kolloquium: Prof. Dr. Ben Harris, Simon's Rock

Vortrag: The Geometry of Characters of Reductive Groups

Abstract:

Let $f$ be a smooth function on a compact, connected Lie group $G$. The Fourier coefficients of $f$ are obtained by convolving the function $f$ with each irreducible character of $G$. Therefore, the irreducible characters of $G$ are the fundamental objects of harmonic analysis on $G$. More generally, for a real reductive group $G$ acting on a homogeneous space $X$, the irreducible characters of $G$ are important for Fourier analysis on $X$, though the precise relationship is more complicated.

                 

In this talk, we discuss how to study irreducible characters geometrically. More precisely, we first recall the Harish-Chandra/Kirillov character formula which writes the irreducible characters of a compact Lie group as Fourier transforms of invariant measures on coadjoint orbits. Then we discuss generalizations to real, reductive groups including recent joint work with Yoshiki Oshima.

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