If (π, V ) is an admissible representation of a p-adic reductive group G and P = MN is a parabolic subgroupwith unipotent radicalN , its Jacquet module VN is the universalN -trivial quotientH0(N,V ) of V by the span of vectors π(n)v − v (n ∈ N ). One fundamental property is that V VN is an exact functor. This construction plays an important role in homomorphisms into representations induced fro...

A bstract We propose magnetic quivers for partial implosion spaces. Such implosions involve a choice of parabolic subgroup, with the Borel subgroup corresponding to standard implosion. In subregular case we test conjecture by verifying that reduction Levi group gives appropriate nilpotent orbit closure. hook diagram are also able carry out this verification provided work at nonzero Fayet-Iliopo...

In this paper, we investigate boundaries of parabolic subgroups of Coxeter groups. Let (W, S) be a Coxeter system and let T be a subset of S such that the parabolic subgroup WT is infinite. Then we show that if a certain set is quasi-dense in W , then W∂Σ(WT , T ) is dense in the boundary ∂Σ(W, S) of the Coxeter system (W, S), where ∂Σ(WT , T ) is the boundary of (WT , T ).

3.3. The greatest common divisor and the least common multiple 12 3.4. Parabolic divisors 14 3.5. Divisibility: further properties 14 4. Normal forms arising from HNN extensions 16 4.1. HNN -normal form 16 5. Conjugacy problem 18 5.1. Conjugacy Criterion for HNN -extensions 18 5.2. Block decomposition 22 5.3. Conjugacy with respect to a subgroup 23 5.4. An algorithm for solving the Conjugacy Pr...

Parabolic geometries may be considered as curved analogues of the homogeneous spaces G/P where G is a semisimple Lie group and P ⊂ G a parabolic subgroup. Conformal geometries and CR geometries are examples of such structures. We present a uniform description of a calculus, called tractor calculus, based on natural bundles with canonical linear connections for all parabolic geometries. It is sh...

In the present paper we continue project of systematic construction invariant differential operators on example non-compact algebra so∗(10). We use maximal Heisenberg parabolic subalgebra P=M⊕A⊕N with M=su(3,1)⊕su(2)≅so∗(6)⊕so(3). give main and reduced multiplets indecomposable elementary representations. This includes explicit parametrization intertwining between ERS. Due to recently establish...

Presentations \\ a la Coxeter" are given for all (irreducible) nite complex reeec-tion groups. They provide presentations for the corresponding generalized braid groups (still conjectural in some cases) which allow us to generalize some of the known properties of nite Coxeter groups (center of the braid group, construction of Hecke algebras). 1. Background from complex reflection groups For all...

In the first part of these notes we shall try to describe the main ideas in the theory. Let G be a reductive algebraic matrix group over Q. Then G(A) is the restricted direct product over all valuations v of the groups G(Qu). If v is finite, define Ku to be G(uJ if this latter group is a special maximal compact subgroup of G(Qu). This takes care of almost all v. For the remaining finite v, we l...

Let G be a split semisimple algebraic group over an arbitrary field F , let E be a G-torsor over F , and let P be a parabolic subgroup of G. The quotient variety X := E/P , known as a flag variety, is generically split, if the parabolic subgroup P is special. It is generic, provided that the G-torsor E over F is a standard generic Gk-torsor for a subfield k ⊂ F and a split semisimple algebraic ...

In this article, we investigate the parabolic logistic equation with blow-up initial and boundary values over a smooth bounded domain Ω: ( ut −∆u = a(x, t)u− b(x, t)u in Ω× (0, T ), u =∞ on ∂Ω× (0, T ) ∪ Ω× {0}, where T > 0 and p > 1 are constants, a and b are continuous functions, with b > 0 in Ω × [0, T ), b(x, T ) ≡ 0. We study the existence and uniqueness of positive solutions, and their as...