scholarly journals Unitary representations induced from maximal parabolic subgroups

1986 ◽  
Vol 69 (1) ◽  
pp. 21-120 ◽  
Author(s):  
M.W Baldoni-Silva ◽  
A.W Knapp
Keyword(s):  
Unitary Representations ◽  
Parabolic Subgroups ◽  
Maximal Parabolic Subgroups

scholarly journals Tight Quotients and Double Quotients in the Bruhat Order

10.37236/1871 ◽  
2005 ◽  
Vol 11 (2) ◽  
Author(s):  
John R. Stembridge
Keyword(s):  
Coxeter Groups ◽  
Upper Bounds ◽  
Bruhat Order ◽  
Weyl Groups ◽  
Order Dimension ◽  
Parabolic Subgroups ◽  
Affine Weyl Groups ◽  
Positive Side ◽  
Maximal Parabolic Subgroups

It is a well-known theorem of Deodhar that the Bruhat ordering of a Coxeter group is the conjunction of its projections onto quotients by maximal parabolic subgroups. Similarly, the Bruhat order is also the conjunction of a larger number of simpler quotients obtained by projecting onto two-sided (i.e., "double") quotients by pairs of maximal parabolic subgroups. Each one-sided quotient may be represented as an orbit in the reflection representation, and each double quotient corresponds to the portion of an orbit on the positive side of certain hyperplanes. In some cases, these orbit representations are "tight" in the sense that the root system induces an ordering on the orbit that yields effective coordinates for the Bruhat order, and hence also provides upper bounds for the order dimension. In this paper, we (1) provide a general characterization of tightness for one-sided quotients, (2) classify all tight one-sided quotients of finite Coxeter groups, and (3) classify all tight double quotients of affine Weyl groups.

scholarly journals Eisenstein Series Arising from Jordan Algebras

2019 ◽  
Vol 72 (1) ◽  
pp. 183-201 ◽  
Author(s):  
Marcela Hanzer ◽  
Gordan Savin
Keyword(s):  
Eisenstein Series ◽  
Jordan Algebra ◽  
Jordan Algebras ◽  
Algebra Structure ◽  
Parabolic Subgroups ◽  
Automorphic Representations ◽  
Unipotent Radicals ◽  
Maximal Parabolic Subgroups

AbstractWe describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

scholarly journals On (2, 3, 7)-generation of maximal parabolic subgroups

2001 ◽  
Vol 71 (2) ◽  
pp. 187-200 ◽  
Author(s):  
L. Di Martino ◽  
M. C. Tamburini
Keyword(s):  
Parabolic Subgroups ◽  
Finitely Generated ◽  
Maximal Parabolic Subgroups

AbstractLet R be a ring with 1 and En (R) be the subgroup of GLn(R) generated by the matrices I + reij, r ∈ R, i ≠ j. We prove that the subgroup of consisting of the matrices of shape , where and , is (2, 3, 7)-generated whenever R is finitely generated and n, are large enough.

scholarly journals Unitary representations with Dirac cohomology: A finiteness result for complex Lie groups

2020 ◽  
Vol 32 (4) ◽  
pp. 941-964 ◽  
Author(s):  
Jian Ding ◽  
Chao-Ping Dong
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Equivalence Classes ◽  
Unitary Representations ◽  
Parabolic Subgroups ◽  
Dirac Cohomology ◽  
Finiteness Result ◽  
Irreducible Unitary Representations ◽  
Cohomological Induction ◽  
Good Range

AbstractLet G be a connected complex simple Lie group, and let {\widehat{G}^{\mathrm{d}}} be the set of all equivalence classes of irreducible unitary representations with non-vanishing Dirac cohomology. We show that {\widehat{G}^{\mathrm{d}}} consists of two parts: finitely many scattered representations, and finitely many strings of representations. Moreover, the strings of {\widehat{G}^{\mathrm{d}}} come from {\widehat{L}^{\mathrm{d}}} via cohomological induction and they are all in the good range. Here L runs over the Levi factors of proper θ-stable parabolic subgroups of G. It follows that figuring out {\widehat{G}^{\mathrm{d}}} requires a finite calculation in total. As an application, we report a complete description of {\widehat{F}_{4}^{\mathrm{d}}}.

scholarly journals PARABOLIC GROUPS ACTING ON ONE-DIMENSIONAL COMPACT SPACES

2005 ◽  
Vol 15 (05n06) ◽  
pp. 893-906
Author(s):  
FRANÇOIS DAHMANI
Keyword(s):  
Hyperbolic Group ◽  
Surface Groups ◽  
Parabolic Subgroups ◽  
Maximal Parabolic Subgroup ◽  
One Dimensional ◽  
Compact Spaces ◽  
Dimensional Boundary ◽  
Relatively Hyperbolic Group ◽  
Relatively Hyperbolic ◽  
Maximal Parabolic Subgroups

Given a class of compact spaces, we ask which groups can be maximal parabolic subgroups of a relatively hyperbolic group whose boundary is in the class. We investigate the class of one-dimensional connected boundaries. We get that any non-torsion infinite finitely-generated group is a maximal parabolic subgroup of some relatively hyperbolic group with connected one-dimensional boundary without global cut point. For boundaries homeomorphic to a Sierpinski carpet or a 2-sphere, the only maximal parabolic subgroups allowed are virtual surface groups (hyperbolic, or virtually ℤ + ℤ).

Rank One Reducibility for Metaplectic Groups via Theta Correspondence

2011 ◽  
Vol 63 (3) ◽  
pp. 591-615 ◽  
Author(s):  
Marcela Hanzer ◽  
Goran Muić
Keyword(s):  
Parabolic Subgroups ◽  
Orthogonal Groups ◽  
Metaplectic Groups ◽  
Theta Correspondence ◽  
Rank One ◽  
Maximal Parabolic Subgroups ◽  
Cuspidal Representations

Abstract We calculate reducibility for the representations of metaplectic groups induced from cuspidal representations of maximal parabolic subgroups via theta correspondence, in terms of the analogous representations of the odd orthogonal groups. We also describe the lifts of all relevant subquotients.

scholarly journals Character tables of the maximal parabolic subgroups of the Ree groups 2F4(q2)

2010 ◽  
Vol 13 ◽  
pp. 90-110 ◽  
Author(s):  
Frank Himstedt ◽  
Shih-Chang Huang
Keyword(s):  
Irreducible Character ◽  
Conjugacy Classes ◽  
Unipotent Radical ◽  
Parabolic Subgroups ◽  
Character Tables ◽  
Maximal Parabolic Subgroups

AbstractWe compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of the simple Ree groups2F4(q2). For one of the maximal parabolic subgroups, we find an irreducible character of the unipotent radical that does not extend to its inertia subgroup.

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