Related papers: Higher Orbital Integrals on Motion Groups and Mack…

We give a coadjoint orbit's diffeomorphic deformation between the classical semisimple case and the semi-direct product given by a Cartan decomposition. The two structures admit the Hermitian symplectic form defined in a semisimple complex…

Let G be a semi-simple Lie group and Q a parabilic subgroup of its complexification G^\mathbb C, then Z:=G^\mathbb C/Q is a compact complex homogeneous manifold. Moreover, G as well as K^\mathbb C, the complexification of the maximal…

We characterize those regular, holomorphic or formal maps into the orbit space $V/G$ of a complex representation of a finite group $G$ which admit a regular, holomorphic or formal lift to the representation space $V$. In particular, the…

Connecting orbits are important invariant structures in the state space of nonlinear systems and various techniques are designed for their computation. However, a uniform analytic approximation of the whole orbit seems rare. Here, based on…

We relate a Chaplygin type system to a Cartan decomposition of a real semi-simple Lie group. The resulting system is described in terms of the structure theory associated to the Cartan decomposition. It is shown to possess a preserved…

Lie-integration is one of the most efficient algorithms for numerical integration of ordinary differential equations if high precision is needed for longer terms. The method is based on the computation of the Taylor-coefficients of the…

Given an orthogonal representation of a compact group, we show that any element of the connected component of the isometry group of the orbit space lifts to an equivariant isometry of the original Euclidean space. Corollaries include a…

We extend the modular orbits method of constructing a two-dimensional orbifold conformal field theory to higher genus Riemann surfaces. We find that partition functions on surfaces of arbitrary genus can be constructed by a straightforward…

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…

The orbit decomposition is given under the automorphism group on the real split Jordan algebra of all hermitian matrices of order three corresponding to any real split composition algebra, or the automorphism group on the complexification,…

Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…

Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. In particular, we compute orbits…

In the present work, we study Hamiltonian systems on (co)adjoint orbits and propose a Lax pair formalism for Gelfand-Tsetlin integrable systems defined on (co)adjoint orbits of the compact Lie groups ${\rm{U}}(n)$ and ${\rm{SO}}(n)$. In the…

In this paper we consider some global constructions of liftings of automorphic representations attached to some commuting pairs in the exceptional group $F_4$. We consider two families of integrals. The first uses the minimal representation…

Some aspects of phase transitions can be more conveniently studied in the orbit space of the action of the symmetry group. After a brief review of the fundamental ideas of this approach, I shall concentrate on the mathematical aspect and…

We study in detail the form of the orbits in integrable generalized H\'enon-Heiles systems with Hamiltonians of the form $H = \frac{1}{2}(\dot{x}^2 + Ax^2 + \dot{y}^2 + By^2) + \epsilon(xy^2 + \alpha x^3).$ In particular, we focus on the…

We study the action of a real reductive group $G$ on a real submanifold $X$ of a Kahler manifold $Z$. We suppose that the action of a compact connected Lie group $U$ with Lie algebra $\mathfrak{u}$ extends holomorphically to an action of…

Conjugation coactions of the quantum general linear group on the algebra of quantum matrices have been introduced in an earlier paper and the coinvariants have been determined. In this paper the notion of orbit is considered via co-orbit…

We have developed a McMurchie-Davidson-like recursion formula for efficient evaluation of the Coulomb attraction and interaction matrix elements between two-dimensional primitive Cartesian Gaussian type orbitals. We also present recurrence…

A Cartan decomposition for symmetric pairs plays an important role to study not only orbit geometry of the symmetric spaces but also harmonic analysis on them. For non-symmetric reductive pairs, there are examples of generalizations of…