There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n are among the very few possibilities of the so called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1, n)/P with a suitable parabolic subgroup P . We s...

In their study of the equivariant K-theory generalized flag varieties G/P, where G is a complex semisimple Lie group, and P parabolic subgroup G, Lenart Postnikov introduced combinatorial tool, called alcove path model. It provides model for highest weight crystals with dominant integral weights, generalizing by semistandard Young tableaux. this paper, we prove simple explicit formula describin...

Let H be the hyperbolic 3-space and IsomH be the group of isometries of H. Let G be a discrete subgroup of IsomH. The action of G on H extends to a continuous action on the compactification of H by the sphere at infinity S ∞. The limit set Λ(G) is the set of all accumulation points of the orbit of a point in H. The limit set does not depend on the choice of the point in H and the limit set is a...

The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over p-adic groups of characteristic zero is studied. The components of representations induced from discrete series of proper parabolic subgroups are classified in terms of R-groups. Multiplicity one is proved. The tempered elliptic spectrum is identified, and the relation ...

Abstract We construct examples of p -adic L -functions over universal deformation spaces for $${{\,\mathrm{GL}\,}}_2$$ GL 2 . formulate a conjecture predicting that the natural parameter and Euler systems are not usual eigenvarietie...

Let G be a complex simple algebraic group and let g be its Lie algebra. A nilpotent orbit O in g is an orbit of a nilpotent element of g by the adjoint action of G on g. Then O admits a natural symplectic 2-form ω and the nilpotent orbit closure Ō has symplectic singularities in the sense of [Be] and [Na3] (cf. [Pa], [Hi]). In [Ri], Richardson introduced the notion of so-called the Richadson or...

Let G be a simple linear algebraic group defined over the field of complex numbers. Fix a proper parabolic subgroup P of G, and also fix a nontrivial antidominant character χ of P . We prove that a holomorphic principal G–bundle EG over a connected complex projective manifold M is semistable satisfying the condition that the second Chern class c2(ad(EG)) ∈ H (M, Q) vanishes if and only if the l...

Let G be a complex, connected, reductive algebraic group. In this paper we show analogues of the computations by Borho and MacPherson of the invariants and antiinvariants of the cohomology of the Springer fibres of the cone of nilpotent elements, N , of Lie(G) for the Steinberg variety Z of triples. Using a general specialization argument we show that for a parabolic subgroup WP ×WQ of W × W th...

A bstract . Let G0 be a real semisimple Lie group, let R be a parabolic subgroup of the complexification G of G0 , let D be an open G0-orbit in the complex flag manifold X = G/R, and let Y be a maximal compact linear subvariety of D. First, an explicit parabolic subgroup Q ⊂ R ⊂ G is constructed so that the open G0-orbits on W = G/Q are measurable and one such orbit D̃ = G0(w) ⊂ W maps onto D wi...

We consider the intersection of pairs of subgroups of a Kleinian group of the second kind K whose limit sets intersect, where one subgroup G is analytically finite and the other J is geometrically finite, possibly infinite cyclic. In the case that J is infinite cyclic generated by M , we show that either some power of M lies in G or there is a doubly cusped parabolic element Q of G with the sam...