Fourier transforms of intertwining operators and Plancherel measures for GL(n). (English) Zbl 0567.22008

Shahidi, Freydoon

Am. J. Math. 106, 67-111 (1984).

The author studies local L-functions of admissible representations of \(GL_ n\) over nonarchimedian local fields. He compares local coefficients of two types: one defined in the context of L-function attached to a pair of representations of general linear groups, and another one defined via intertwining operators. The main result of the paper is that these two local coefficients are equal. Using this theorem, the author obtains a formula for the Plancherel measure on \(GL_ n\) over a local nonarchimedian field.

Reviewer: S.I.Gel’fand

MSC:

22E50

Representations of Lie and linear algebraic groups over local fields

Keywords:

local L-functions; representations of \(GL_ n\); nonarchimedian local fields; intertwining operators; Plancherel measure