Related papers: Regular functions on covers of nilpotent coadjoint…

For an irreducible smooth representation of a connected reductive $p$-adic group, two important associated invariants are the wavefront set and the (partly conjectural) Langlands parameter. While a wavefront set consists of $p$-adic…

Harmonic functions of the three dimensional Lie groups defined on certain manifolds related to the Lie groups themselves and carrying all their unitary representations are explicitly constructed. The realisations of these Lie groups are…

This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…

This is the first in a series of papers devoted to an analogue of the metaplectic representation, namely, the minimal unitary representation of an indefinite orthogonal group; this representation corresponds to the minimal nilpotent…

In the classification of stationary solutions in extended supergravities with symmetric scalar manifolds, the nilpotent orbits of a real symmetric pair play an important role. In this paper we discuss two approaches to determining the…

We apply the orbit method to obtain formula for multiplicities of certain representations of unipotent groups over the finite field.

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…

We construct by geometric methods a noncommutative model E of the algebra of regular functions on the universal (2-fold) cover M of certain nilpotent coadjoint orbits O for a complex simple Lie algebra g. Here O is the dense orbit in the…

We present the classification of coadjoint orbits of the unitriangular group $UT(7, K)$. We also describe subregular orbits of $UT(n, K)$ for an arbitrary $n$.

In these notes we consider power series representations of functions on the unit disk in the complex plane which define harmonic and holomorphic functions and related matters concerning boundary values, Poisson kernels, and so on.

We study the space of invariant generalized functions supported on an orbit of the action of a real algebraic group on a real algebraic manifold. This space is equipped with the Bruhat filtration. We study the generating function of the…

We study the regular function ring $R(\mathcal{O})$ for all symplectic nilpotent orbits $\mathcal{O}$ with even column sizes. We begin by recalling the quantization model for all such orbits by Barbasch using unipotent representations. With…

The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.

In this paper we describe a multiparameter deformation of the function algebra of a semisimple coadjoint orbit. In the first section we use the representation of the Lie algebra on a generalized Verma module to quantize the Kirillov bracket…

In this paper we derive an explicit expression for the normal zeta function of class two nilpotent groups whose associated Pfaffian hypersurface is smooth. In particular, we show how the local zeta function depends on counting mod p…

Let $G$ be a semisimple simply connected algebraic group over ${\mathbb C}$ of exceptional type. For each $G$-equivariant nilpotent cover of a nilpotent coadjoint $G$-orbit ${\mathbb O}$, we determine the unique birationally rigid induction…

Let $F$ be a non-Archimedean local field and let $\mathcal{O}_{F}$ be its ring of integers. The orbit of an irreducible representation $\rho$ of $\mathrm{GL}_n(\mathcal{O}_F)$ is a conjugacy class in $\mathfrak{gl}_n(\mathcal{O}_F)$…

In this paper decomposition of periodic orbits in bifurcation diagrams are derived in unidimensional dynamics system $x_{n+1}=f(x_{n};r)$, being $f$ an unimodal function. We proof a theorem which states the necessary and sufficient…

We consider groupoids constructed from a finite number of commuting local homeomorphisms acting on a compact metric space, and study generalized Ruelle operators and $ C^{\ast} $-algebras associated to these groupoids. We provide a new…

Nilpotent Lie groups with stepwise square integrable representations were recently investigated by J.A.~Wolf. We give an alternative approach to these representations by relating them to the stratifications of the duals of nilpotent Lie…