Related papers: Oscillator algebras with semi-equicontinuous coadj…

This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent…

Motivated by the recent rapid development of complexity theory applied to quantum mechanical processes we present the complete derivation of Nielsen's complexity of unitaries belonging to the representations of oscillator group. Our…

We study deformations of orbit closures for the action of a connected semisimple group $G$ on its Lie algebra $\mathfrak{g}$, especially when $G$ is the special linear group. The tools we use are on the one hand the invariant Hilbert scheme…

We consider a family of Hecke C*-algebras which can be realised as crossed products by semigroups of endomorphisms. We show by dilating representations of the semigroup crossed product that the category of representations of the Hecke…

The Oscillator Groups,$\G_\lambda,$ are the only solvable, non commutative, simply connected Lie groups to admit a Lorentzian bi-invariant metric. For these groups, we give sufficient conditions for a left-invariant pseudo-Riemannian metric…

A host algebra of a topological group G is a C^*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite…

Let V be a standard subspace in the complex Hilbert space H and U : G \to U(H) be a unitary representation of a finite dimensional Lie group. We assume the existence of an element h in the Lie algebra of G such that U(exp th) is the modular…

Let $H$ be an infinite dimensional separable Hilbert space, $B(H)$ the $C^*$-algebra of all bounded linear operators on $H,$ $U(B(H))$ the unitary group of $B(H)$ and ${\cal K}\subset B(H)$ the ideal of compact operators. Let $G$ be a…

An algebraic group is called semi-reductive if it is a semi-direct product of a reductive subgroup and the unipotent radical. Such a semi-reductive algebraic group naturally arises and also plays a key role in the study of modular…

We derive manifestly covariant actions of spinning particles starting from coadjoint orbits of isometry groups, by using Hamiltonian reductions. We show that the defining conditions of a classical Lie group can be treated as Hamiltonian…

We consider the (extended) metaplectic representation of the semidirect product $\mathcal{G}={\mathbb H}^d\rtimes Sp(d,{\mathbb R})$ between the Heisenberg group and the symplectic group. Subgroups $H=\Sigma \rtimes D$, with $\Sigma$ being…

In this note the smooth (i.e. with open stabilizers) linear and {\sl semilinear} representations of certain permutation groups (such as infinite symmetric group or automorphism group of an infinite-dimensional vector space over a finite…

In the previous works \cite{N46,N47} authors have defined the oscillator-like system that associated with the two variable Chebyshev-Koornwinder polynomials. We call this system the generalized Chebyshev - Koornwinder oscillator. In this…

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type,…

If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a…

Orbits of coadjoint representations of classical compact Lie groups have a lot of applications. They appear in representation theory, geometrical quantization, theory of magnetism, quantum optics etc. As geometric objects the orbits were…

We study two classes of operator algebras associated with a unital subsemigroup $P$ of a discrete group $G$: one related to universal structures, and one related to co-universal structures. First we provide connections between universal…

We consider the groups G which arise from real semisimple Jordan algebras via the Tits-Koecher-Kantor construction. Such a G is characterized by the fact that it admits a parabolic subgroup P=LN which is conjugate to its opposite, and for…

A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend…

We examine a new application of the Holstein-Primakoff realization of the simple harmonic oscillator Hamiltonian. This involves the use of infinite-dimensional representations of the Lie algebra $su(2)$. The representations contain…