@techreport{577185acec8c47d9ae24fb0ef9b683a1,

title = "Fourier transforms on the basic affine space of a quasi-split group",

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 $G\times T$ 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 $G\times (T\rtimes W)$ 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.",

keywords = "Mathematics - Representation Theory, 22E50",

author = "Nadya Gurevich and David Kazhdan",

year = "2019",

language = "???core.languages.en_GB???",

series = "Arxiv preprint",

edition = "arXiv:1912.07071 [math.RT]",

type = "WorkingPaper",

}