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- W2996516951 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 $Gtimes T$ 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 $Gtimes (Trtimes W)$ by generalized Fourier transforms $Phi_w$. We define an analog of these operators for quasi-split groups. We also extend the construction of the Schwartz space $mathcal S (X)$ by Braverman and Kazhdan to the case of quasi-split groups." @default.
- W2996516951 created "2019-12-26" @default.
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- W2996516951 date "2019-12-15" @default.
- W2996516951 modified "2023-09-27" @default.
- W2996516951 title "Fourier transforms on the basic affine space of a quasi-split group." @default.
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