ALGÈBRES DE HECKE ET SÉRIES PRINCIPALES GÉNÉRALISÉES DE Sp<sub>4</sub>(<i>F</i>)
Abstrak
The aim of this work is to expand Bushnell and Kutzko's theory of $G$-covers [Proc. London Math. Soc. 77 (1998) 582–634] up to a full description of the generalized principal series of the $p$-adic group ${\rm Sp}_4(F)$, with $p$ odd.We start with a Levi component $M$ of a maximal parabolic subgroup $P$ of $G = {\rm Sp}_4(F)$ and an explicit type $(J_M, \tau_M)$ for the inertial class $S$ in $M$ of a supercuspidal representation of $M$. We compute the Hecke algebra of a $G$-cover $(J, \tau)$ of $(J_M, \tau_M)$ constructed in our previous work [Ann. Inst. Fourier 49 (1999) 1805–1851]: it is a convolution algebra on a Coxeter group (namely, the affine Weyl group of either $U(1,1)(F)$, in the case of the Siegel parabolic, or ${\rm SL}_2(F)$), described explicitly by generators and relations.From this and Bushnell and Kutzko's work we derive the structure of the parabolically induced representations ${\rm ind}_P^G \pi$, for $\pi$ in $S$, and we find their discrete series subrepresentations if any, thus recovering, through the theory of $G$-covers, results previously obtained by Shahidi using different methods.The paper is written in French.2000 Mathematical Subject Classification: 22E50, 11F70.
Penulis (2)
LAURE BLASCO
CORINNE BLONDEL
Akses Cepat
- Tahun Terbit
- 2002
- Bahasa
- en
- Total Sitasi
- 7×
- Sumber Database
- CrossRef
- DOI
- 10.1112/s0024611502013667
- Akses
- Open Access ✓