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{\Large Department of Mathematics, BGU}

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{\Huge AGNT}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, December 25, 2019}
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\textbf{At} \emph{15:00 -- 16:15}
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\textbf{In} \emph{-101}

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{\large\scshape Nadya Gurevich 
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  (BGU)
}
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will talk about
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{\Large\bfseries Fourier transforms on the basic affine space\par}
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\textsc{Abstract:}
For a quasi-split group \$G\$ over a local field \$F\$, with Borel subgroup \$B=TU\$ and Weyl group \$W\$,
 there is a natural geometric action of \$G\textbackslash{}times T\$ on \$L\^{}2(X),\$ where \$X=G/U\$ is the basic affine space of \$G\$.
For split groups, Gelfand and Graev have extended this action to an action of
\$G\textbackslash{}times (T\textbackslash{}rtimes W)\$  by  generalized Fourier transforms \$\textbackslash{}Phi\_w\$.  We shall extend this result for  quasi-split groups, using a new interpretation
of Fourier transforms for quasi-split groups
of rank one.

This is joint work with David Kazhdan.








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