Eisenstein Series Arising from Jordan Algebras

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

Residues of standard intertwining operators on p-adic classical groups

We study two basic problems involved in the study of the standard intertwining operators attached to representations induced from irreducible unitary supercuspidal representations on maximal parabolic subgroups of

Rank One Reducibility for Metaplectic Groups via Theta Correspondence

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.

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

We 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.

Normal Structure of Maximal Parabolic Subgroups in Chevalley Groups over Rings

We study the normal structure of maximal parabolic subgroups of a Chevalley group over a commutative ring. More precisely, we describe the subgroups of a maximal parabolic subgroup P normalized by the elementary part of its Levi subgroup. As a corollary, we obtain a description of the subgroups in P normalized by its elementary subgroup EP.

PARABOLIC GROUPS ACTING ON ONE-DIMENSIONAL COMPACT SPACES

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).

Tight Quotients and Double Quotients in the Bruhat Order

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.

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

Let 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.