On the gamma factors attached to representations of \(U(2,1)\) over a \(p\)-adic field (Q1376055)

This paper is mainly devoted to developing the local theory of generic representations of a group of the form \(U(2,1)\) defined with respect to a quadratic extension of non-archimedean local fields. The author develops the basic theory, augments this with a theory of the structure of such representations and deduces that the gamma function of a representation determines it completely. This fact was already known; it is due to \textit{S. Gelbart}, \textit{J. Rogawski} and \textit{D. Soudry} [C. R. Acad. Sci., Paris, Sér. I 317, 717-722 (1993; Zbl 0807.11028)], who used global methods. The author also gives a global application (also due, with different methods, to Gelbart, Rogawski and Soudry (loc. cit.)).