Irreducibility of the analytic continuation of the principal series of a free group

Anna Maria Mantero, Anna Zappa

Type: Article

Publication Date: 1987-10-01

Citations: 3

DOI: https://doi.org/10.1017/s1446788700029335

Abstract

In this paper it is proved that the principal series of representations of Γ = Z 2 *…*Z 2 may be analytically continued to give uniformly bounded representations on the same Hilbert space, and that these representations are irreducible . Further, the reducibility of the restrictions to Γ ⊂ SL (2, Q p ) of the irreducible unitary representations of SL(2, Q p ) is examined.

Locations

Journal of the Australian Mathematical Society Series A Pure Mathematics and Statistics - View - PDF

Similar Works

Action	Title	Year	Authors
+	On the irreducibility of unitary principal series representations	1982	Dragan Miličić Mirko Primc
+ PDF Chat	Analytic continuation of the principal series	1961	Ray A. Kunze E. M. Stein
+	Analytic continuation of group representations	1978	Meir Shinnar
+	Analytic continuation of group representations	1970	Elias M. Stein
+	Analytic continuation of group representations	1967	Elias M. Stein
+	On irreducibility of the principal series	1977	Jacques Carmona
+	Reducibility of generalized principal series representations of $U(2, 2)$ via base change	1993	David Theo Goldberg
+ PDF Chat	Analytic continuation of group representations. III	1966	Róbert Hermann
+	Reduction of the principal series representation of Lorentz groups on an Abelian subgroup	1980	Ali Reza Assar
+	Limits of Discrete Series for the Lorentz Groups (ユニタリ表現論とその応用)	1973	俊昭米山
+	On the existence of homomorphisms between principal series of complex semisimple Lie groups = 複素半単純リー群の主系列表現の間の準同型の存在について	2008	紀行阿部
+	Reducibility of representations induced from the Zelevinsky segment and discrete series	2020	Ivan Matić
+	PRINCIPAL SERIES OF UNITARY IRREDUCIBLE REPRESENTATIONS	1970	A. Esteve A. Tiemblo
+	The complex analytic extension of the Fourier series on lie groups	1975	Luis A. Forta-Mattos
+	Irreducibility theorems for the principal series	1972	Anthony W. Knapp E. M. Stein
+ PDF Chat	Analytic continuation of group representations	1966	Róbert Hermann
+ PDF Chat	Boundary behavior of limits of discrete series representations of real rank one semisimple groups	1986	Brian E. Blank
+	Principal series representations of finite Chevalley groups	1978	Robert W. Kilmoyer
+	Polyhedral Summability of Fourier Series on Compact Lie Groups	1978	Robert J. Stanton Peter A. Tomas
+	Infinite irreducible representations of the Lorentz group	1984	Harish-chandra Harish-Chandra

Works That Cite This (3)

Action	Title	Year	Authors
+ PDF Chat	Equivalence of two series of spherical representations of a free group	1993	Anna Maria Mantero Tadeusz Pytlik Ryszard Szwarc Anna Zappa
+ PDF Chat	Spherical functions and uniformly bounded representations of free groups	1991	Tadeusz Pytlik
+ PDF Chat	Anisotropic principal series and generators of a free group	1994	Carlo Pensavalle

Works Cited by This (22)

Action	Title	Year	Authors
+	Sur les représentations uniformément bornées et le théorème de convolution de Kunze-Stein	1981	Noël Lohoué
+	Representations spheriques uniformement bornees des groupes de Lorentz	1979	Lucien Bamazi
+ PDF Chat	Restriction of spherical representations of 𝑃𝐺𝐿₂(𝑄_{𝑝}) to a discrete subgroup	1984	Alessandro Figà-Talamanca Massimo A. Picardello
+	Representation theory and automorphic functions	1969	М. И. Граев Ilya Piatetski-Shapiro I. M. Gel'fand K. A. Hirsch
+	Harmonic analysis on SL(n, C)	1969	Ronald L. Lipsman
+ PDF Chat	Uniformly bounded representations for the Lorentz groups	1972	Edward N. Wilson
+	Spherical functions and harmonic analysis on free groups	1982	Alessandro Figà-Talamanca Massimo A. Picardello
+	The Poisson transform and representations of a free group	1983	Anna Maria Mantero Anna Zappa
+	Analytic continuation of the irreducible unitary representations of the universal covering group of 𝑆𝐿(2,𝑅)	1967	Paul Sally
+ PDF Chat	Special series of unitary representations of groups acting on homogeneous trees	1986	Anna Maria Mantero Anna Zappa