This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup ofM gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural...

We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and Ρ a parabolic subgroup of G. To this end we compare two descriptions of the cohomology of such spaces. One of these makes use of the partition of G/P into cells (Schubert cells), while the other consists in identifying the cohomology of G/P with certain polynomials on the Lie algebra of th...

We study automorphisms of a relatively hyperbolic group G. When G is oneended, we describe Out(G) using a preferred JSJ tree over subgroups that are virtually cyclic or parabolic. In particular, when G is toral relatively hyperbolic, Out(G) is virtually built out of mapping class groups and subgroups of GLn(Z) fixing certain basis elements. When more general parabolic groups are allowed, these ...

We give a necessary and sufficient condition for pair of parabolic subgroups $P$ $Q$ $G=GL_n(\mathbb{R})$ such that the tensor product any two unitarily induced representations from are tempered. also an $L^p$-estimate matrix coefficients regular on $L^2(G/L)$ when $L$ is Levi subgroup $G$.

We study the properties of groups that have presentations in which generating set is a fixed involutions and all additional relations are even length. consider parabolic subgroups such group show every element has factorization with respect to given subgroup. Furthermore, we give counterexample, using cluster presentation, demonstrates this not necessarily unique.

We study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K\G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic...

The smallest known thick generalized octagon has order (2,4) and can be constructed from the parabolic subgroups of the Ree group 2F4(2). It is not known whether this generalized octagon is unique up to isomorphism. We show that it is unique up to isomorphism among those having a point a whose stabilizer in the automorphism group both fixes setwise every line on a and contains a subgroup that i...

Let q be a power of a prime p. Let P be a parabolic subgroup of the general linear group GLn(q) that is the stabilizer of a flag in F n q of length at most 5, and let U = Op(P ). In this note we prove that, as a function of q, the number k(U) of conjugacy classes of U is a polynomial in q with integer coefficients.

This note is devoted to study an inverse Cauchy problem in a Hilbert space H for fractional abstract differential equations of the form; ), ( ) ( ) ( = ) ( t g t f t u A dt t u d    with the initial condition H u u = (0) 0 and the overdetermination condition: ), ( = ) ), ( ( t w v t u where (.,.) is the inner product in H , f is a real unknown function w is a given real function, 0 u , v ar...

Define the following parabolic operator in divergence form Lu ≡ ∂u ∂t − ∂ ∂x j a ij (x, t) ∂u ∂x i for (x, t) ∈ Ω T = Ω × (0, T ], where Ω is a bounded simply connected subset of R m for m ≥ 2 and T > 0 is a fixed but arbitrary positive number. We also assume that the a ij are bounded and measurable in ¯ Ω T and satisfy the uniform parabolicity condition: 1/ν |z| 2 ≤ m i,j=1 a ij (x, t)z i z j ...