Related papers: Projective representation theory for compact quant…

We survey some of the known results on the relation between the homology of the {\em full} Hecke algebra of a reductive $p$-adic group $G$, and the representation theory of $G$. Let us denote by $\CIc(G)$ the full Hecke algebra of $G$ and…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

A one to one correspondence between shifts of group-like projections on a locally compact quantum group ${\mathbb{G}}$ which are preserved by the scaling group and contractive idempotent functionals on the dual $\hat{\mathbb{G}}$ is…

The goal of this article is to provide a bridge between the gamma element method for the Baum--Connes conjecture (the Dirac dual-Dirac method) and the controlled algebraic approach of Roe and Yu (localization algebras). For any second…

Consider a compact torsion free CR manifold $X$ and assume that $X$ admits a compact CR Lie group action $G$. Let $L$ be a $G$-equivariant rigid CR line bundle over $X$. It seems natural to consider the space of $G$-invariant CR sections in…

The paper is a survey of recent results in geometric representation theory describing group actions which induce multiplicity-free representations in the spaces of holomorphic functions. For connected compact Lie groups of automorphisms of…

We consider a coamenable compact quantum group $\mathbb{G}$ as a compact quantum metric space if its function algebra $\mathrm{C}(\mathbb{G})$ is equipped with a Lip-norm. By using a projection $P$ onto direct summands of the Peter--Weyl…

Entanglement transformation of composite quantum systems is investigated in the context of group representation theory. Representation of the direct product group $SL(2,C)\otimes SL(2,C)$, composed of local operators acting on the binary…

Singular actions on C*-algebras are automorphic group actions on C*-algebras, where the group need not be locally compact, or the action need not be strongly continuous. We study the covariant representation theory of such actions. In the…

Let G be a real or complex linear algebraic reductive group. Let H and F be reductive subgroups. We study the natural H action on G/F. The main theorem of this note shows that generic H orbits are closed. This theorem is then applied to…

The main result of the paper is the characterization of those locally compact quantum groups with projection, i.e. non-commutative analogs of semidirect products, which are extensions as defined by L. Vainerman and S. Vaes. It turns out…

Let $G$ be a finite group and $H$ a normal subgroup. Starting from $G$-spin models, in which a non-Abelian field ${\mathcal{F}}_H$ w.r.t. $H$ carries an action of the Hopf $C^*$-algebra $D(H;G)$, a subalgebra of the quantum double $D(G)$,…

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible *-representations. Then we study their behaviour under the…

A symmetry in quantum mechanics is described by the projective representations of a Lie symmetry group that transforms between physical quantum states such that the square of the modulus of the states is invariant. The Heisenberg…

The aim of this paper is to show that classical geometric invariant theory (GIT) has an effective analogue for linear actions of a non-reductive algebraic group $H$ with graded unipotent radical on a projective scheme $X$. Here the linear…

In this article, the quantum representation of the algebra among reduced twisted geometries (with respect to the Gauss constraint) is constructed in the gauge invariant Hilbert space of loop quantum gravity. It is shown that the reduced…

We study the dual relationship between quantum group convolution maps $L^1(\mathbb{G})\rightarrow L^{\infty}(\mathbb{G})$ and completely bounded multipliers of $\widehat{\mathbb{G}}$. For a large class of locally compact quantum groups…

We introduce an axiomatization of the notion of a semidirect product of locally compact quantum groups and study properties. Our approach is slightly different from the one introduced in the thesis of S.~Roy and, unlike the investigations…

We introduce quantum tomography on locally compact Abelian groups $G$. A linear map from the set of quantum states on the $C^*$-algebra $A(G)$ generated by the projective unitary representation of $G$ to the space of characteristic…

Let $X$ be a CR manifold with transversal, proper CR $G$-action. We show that $X/G$ is a complex space such that the quotient map is a CR map. Moreover the quotient is universal, i.e. every invariant CR map into a complex manifold…