Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0562.43005
Benoist, Yves
Multiplicité un pour les espaces symétriques exponentiels. (French)
[J] Mém. Soc. Math. Fr., Nouv. Sér. 15, 1-37 (1984). ISSN 0249-633X

The results of this work were announced in the preceding note of the author [C. R. Acad. Sci., Paris, Ser. I 12, 489-492 (1983; Zbl 0529.22009)]. Let G be a Lie group, $\sigma$ be an involution of G, L be the $\sigma$-stable subgroup of G, $\pi$ be a unitary representation of G which admits a cyclic eigenvector of L. A sufficient multiplicity-free condition is given for $\pi$. The main corollary is the following. If G is an exponential group and H is its $\sigma$-fixed point subgroup then the representation $Ind\sp G\sb H(1)$ of G in $L\sp 2(G/H)$ is multiplicity-free. For this case the author points out the orbits in the coadjoint representation corresponding to irreducible unitary representations in the decomposition of $Ind\sp G\sb H(1)$. An example is given, which shows that the statement about $Ind\sp G\sb H(1)$ is false for any solvable Lie group G. Furthermore some results about dimension of the L-eigenvectors space are given.
[V.Molchanov]

MSC 2000:: *43A85 Analysis on homogeneous spaces

Keywords: symmetric spaces; unitary representation; multiplicity-free condition

Citations: Zbl 0529.22009

Cited in: Zbl 0807.22006 Zbl 0714.22007

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]