Related papers: Unitary representations of the quantum "ax+b" grou…

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…

It often goes unnoticed that, even for a finite number of degrees of freedom, the canonical commutation relations have many inequivalent irreducible unitary representations; the free particle and a particle in a box provide examples that…

Compact matrix quantum groups are strongly determined by their intertwiner spaces, due to a result by S.L. Woronowicz. In the case of easy quantum groups, the intertwiner spaces are given by the combinatorics of partitions, see the inital…

We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is…

We consider a constructive modification of quantum-mechanical formalism. Replacement of a general unitary group by unitary representations of finite groups makes it possible to reproduce quantum formalism without loss of its empirical…

We construct, using the quantum dilogarithm, a series of *-representations of quantized cluster varieties. This includes a construction of infinite dimensional unitary projective representations of their discrete symmetry groups - the…

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n-1 quantum groups for q a root of unity. Representations which have the maximal dimension and…

Let G be a special linear group over the real, the complex or the quaternion, or a special unitary group. In this note, we determine all special unipotent representations of G in the sense of Arthur and Barbasch-Vogan, and show in…

Generalizing the notion of continuous Hilbert space representations of compact topological groups we define unitary continuous correpresentations of $C^*$-completions of compact quantum group Hopf algebras on arbitrary Hilbert spaces. It is…

We study projective unitary (co)representations of compact quantum groups and the associated second cohomology theory. We introduce left/right/bi/strongly projective corepresentations and study them in details. In particular, we prove that…

We show that every unitary representation of a solvable discrete virtually nilpotent group G is quasidiagonal. Roughly speaking, this says that every unitary representation of G approximately decomposes as a direct sum of finite dimensional…

We propose a weaker condition for multiplicative unitary operators related to quantum groups, than the condition of manageability introduced by S.L. Woronowicz. We prove that all the main results of the theory of manageable multiplicative…

A group theoretical understanding of the two dimensional fractional supersymmetry is given in terms of the quantum Poincare group at roots of unity. The fractional supersymmetry algebra and the quantum group dual to it are presented and the…

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in…

Associated to a finite graph $X$ is its quantum automorphism group $G$. The main problem is to compute the Poincar\'e series of $G$, meaning the series $f(z)=1+c_1z+c_2z^2+...$ whose coefficients are multiplicities of 1 into tensor powers…

We introduce and study several amenability properties for unitary corepresentations and *-representations of algebraic quantum groups, which may be used to characterize amenability or co-amenability of such groups. As a background for this…

The method of geometrical quantization of symplectic manifolds is applied to constructing infinite dimensional irreducible unitary representations of the algebra of functions on the compact quantum group $SU_q(2)$. A formulation of the…

We show that in the presence of suitable commutator estimates, a projective unitary representation of the Lie algebra of a connected and simply connected Lie group G exponentiates to G. Our proof does not assume G to be finite--dimensional…

This article shows that one can consistently incorporate nonunitary representations of at least one group into the ``ordinary'' nonrelativistic quantum mechanics. This group turns out to be Lorentz group thus giving us an alternative…

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a…