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Every irreducible finite-dimensional representation of the quantized enveloping algebra U_q(gl_n) can be extended to the corresponding quantum affine algebra via the evaluation homomorphism. We give in explicit form the necessary and…

We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf $*$-algebras. Moreover, we characterize invariant inner products…

For a group $G$ definable in a first order structure $M$ we develop basic topological dynamics in the category of definable $G$-flows. In particular, we give a description of the universal definable $G$-ambit and of the semigroup operation…

An oscillator group $G$ is a semidirect product of a Heisenberg group with a one-parameter group. In this article we construct Olshanski semigroups for infinite-dimensional oscillator groups. These are complex involutive semigroups which…

We determine all holomorphically separable complex manifolds of dimension $p+q$ which admits a smooth envelope of holomorphy such that the general indefinite unitary group of size $p+q$ acts effectively by holomorphic transformations. Also…

The group $G_2$ of invertible affine transformations of $\mathbb{R}^2$ has, up to equivalence, one square--integrable representation. Two new realizations of this representation are presented and novel continuous wavelet transforms, acting…

Let $G$ be a metrizable compact group, $A$ a separable C*-algebra and $\alpha$ a strongly continuous action of $G$ on $A$. Provided that $\alpha$ satisfies the continuous Rokhlin property, we show that the property of satisfying the UCT in…

Let $k$ be a local field of characteristic 0, and let $G$ be a connected semisimple almost $k$-algebraic group. Suppose rank$_kG\geq 1$ and $\rho$ is an excellent representation of $G$ on a finite dimensional $k$-vector space $V$. We…

In this paper we prove some general theorems about representations of finite groups arising from the inner semidirect product of groups. We show how these results can be used for standard applications of group theory in quantum chemistry…

Let $G$ be a countable residually finite group (for instance $\mathbb{F}_2$) and let $\overleftarrow{G}$ be a totally disconnected metric compactification of $G$ equipped with the action of $G$ by left multiplication. For every $r\geq 1$ we…

Let $N$ be a simply connected, connected nilpotent Lie group which admits a uniform subgroup $\Gamma.$ Let $\alpha$ be an automorphism of $N$ defined by $\alpha\left( \exp X\right) =\exp AX.$ We assume that the linear action of $A$ is…

We obtain necessary and sufficient conditions for the admissible vectors of a new unitary non irreducible representation $U$. The group $G$ is an arbitrary semidirect product whose normal factor $A$ is abelian and whose homogeneous factor…

We give an elementary analysis of the multiplicator group of the Galilei group in 1+2 dimensions $G^{\uparrow}_{+}$. For a non-trivial multiplicator we give a list of all the corresponding projective unitary irreducible representations of…

Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either with curvature, positive on complex isotropic two-planes, or self-dual of positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary representation, and…

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…

We further investigate the weak topology generated by the irreducible unitary representations of a group $G$. A deep result due to Ernest \cite{Ernest1971} and Hughes \cite{Hughes1973} asserts that every weakly compact subset of a locally…

We study testing properties of functions on finite groups. First we consider functions of the form $f:G \to \mathbb{C}$, where $G$ is a finite group. We show that conjugate invariance, homomorphism, and the property of being proportional to…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

Hilbert--Lie groups are Lie groups whose Lie algebra is a real Hilbert space whose scalar product is invariant under the adjoint action. These infinite-dimensional Lie groups are the closest relatives to compact Lie groups. Here we study…