Results 141 to 150 of about 310,777 (176)

On the structure of parabolic subgroups

Communications in Algebra, 1990
H Azad
exaly   +2 more sources

The Plancherel Formula for parabolic subgroups

Israel Journal of Mathematics, 1977
We prove an explicit Plancherel Formula for the parabolic subgroups of the simple Lie groups of real rank one. The key point of the formula is that the operator which compensates lack of unimodularity is given, not as a family of implicitly defined operators on the representation spaces, but rather as an explicit pseudo-differential operator on the ...
Keene, Frederick W., Lipsman, Ronald L., Wolf, Joseph A.   +2 more
openaire   +1 more source

Parabolic subgroups

2000
Abstract Subgroups that deserve special attention are those which share defining properties of their parent groups. In the case of a Coxeter group W with its distinguished generating set S, a subgroup generated by a subset of S is a Coxeter group in its own right.
Meinolf Geck, Golz Pfeiffer
openaire   +1 more source

The Structure of Parabolic Subgroups

Journal of Lie Theory, 2004
For a real connected simple noncompact Lie group \(G\) with Iwasawa decomposition \(G=KAN\) the structure of the subgroup \(M=Z(A)\cap K\) is known in case \(G\) is a linear group. The subgroup \(B=MAN\) is a minimal parabolic subgroup of \(G\) and since \(A\) is a vector group and \(N\) is simply connected nilpotent, the topological structure of \(B\)
openaire   +2 more sources

Extensions of Homomorphisms of Parabolic Subgroups

Canadian Journal of Mathematics, 1972
If one wishes to construct a homomorphism of a group, an obvious approach is to begin with a homomorphism of a subgroup and attempt to extend it in some way. Any such extended homomorphism is determined by its action on elements of the group which, together with the subgroup ...
openaire   +1 more source

Subalgebras and Parabolic Subgroups

1998
The key to understanding the geometrical structure of the compactifications of symmetric spaces of non-compact type is given by the family of parabolic subgroups of G. In this chapter the relation between these subgroups and sets of simple roots is discussed. Additional details for matters treated in this chapter may be found in Helgason [H2] or Warner
Yves Guivarc’h, Lizhen Ji, J. C. Taylor   +2 more
openaire   +1 more source

The restriction of minuscule representations to parabolic subgroups

Mathematical Proceedings of the Cambridge Philosophical Society, 2003
Let \(G\) be a universal Chevalley group over a field \(F\) of any characteristic, with subfield \(E\), with some mild restrictions on \(E\). One considers an irreducible \(FG(E)\)-module \(V\) whose highest weight \(\lambda\) is minuscule. The following description is developed. The weights of \(V\) form an orbit under the Weyl group \(W\).
Parker, Chris, Roehrle, Gerhard
openaire   +3 more sources

Generalized Hua Operators and Parabolic Subgroups

The Annals of Mathematics, 1984
Let G be a connected non compact semisimple group with finite center, and K a maximal compact subgroup. The space \(\Omega =G/K\) is a Riemannian symmetric space. For a parabolic subgroup P of G one defines the Poisson integral \({\mathcal P}_ P: C^{\infty}(G/P)\to C^{\infty}(\Omega)\). This transform extends to a map from the space \({\mathcal B}(P)\)
openaire   +1 more source

On the nilradical of a parabolic subgroup

2014
We present various approaches to understanding the structure of the nilradical of parabolic subgroups in type A. In particular, we consider the complement of the open dense orbit and describe its irreducible components.
openaire   +1 more source

PARABOLIC SUBGROUPS AND CUSPIDAL REPRESENTATIONS OF FINITE MONOIDS

International Journal of Algebra and Computation, 1991
This paper is mostly concerned with arbitrary finite monoids M with the complex semigroup algebra [Formula: see text] semisimple. Using the 1942 work of Clifford, we develop for these monoids a theory of cuspidal representations. Harish-Chandra's philosophy of cuspidal representations of finite groups can then be derived with an appropriate ...
Jan Okninski, Mohan S. Putcha
openaire   +2 more sources