Contact｜Sitemap｜HOME｜Japanese
HOME > Table of Contents and Abstracts > Vol. 52, No. 1
Tohoku Mathematical Journal
2000
March
SECOND SERIES VOL. 52, NO. 1
Tohoku Math. J.
52 (2000), 127152

Title
ON $\theta$STABLE BOREL SUBALGEBRAS OF LARGE TYPE FOR REAL REDUCTIVE GROUPS
Author
Takuya Ohta
(Received September 17, 1998, revised May 13, 1999) 
Abstract.
VoganZuckerman's standard representation $X$ for a real reductive group $G(\boldsymbol{R})$ is constructed from a $\theta$stable parabolic subalgebra $\mathfrak{q}$ of the complexified Lie algebra $\mathfrak{g}$ of $G(\boldsymbol{R})$. Adams and Vogan showed that the set of $\mathfrak{g}$principal $K$orbits in the associated variety $\mathrm{Ass}(X)$ of $X$ is in onetoone correspondence with the set $\mathcal{B}_{\mathfrak{g}^}^L/K$ of $K$conjugacy classes of $\theta$stable Borel subalgebras of large type having representatives in the opposite parabolic subalgebra $\mathfrak{q}^$ of $\mathfrak{q}$. In this paper, we give a description of $\mathcal{B}_{\mathfrak{q}}^L/K$ and show that $\mathcal{B}_\mathfrak{q}^L/K \ne \emptyset$ under certain condition on the positive system of imaginary roots contained in $\mathfrak{q}$. Furthermore, we construct a finite group which acts on $\mathcal{B}_\mathfrak{q}^L/K$ transitively.
1991 Mathematics Subject Classification.
Primary 17B45; Secondary 22E45, 22E46, 22E47.


To the top of this page
Back to the Contents