相关论文: Free quantum analogue of Coxeter group $D_4$

Using the natural irreducible 8-dimensional representation and the two spin representations of the quantum group $U_q$(D$_4$) of D$_4$, we construct a quantum analogue of the split octonions and study its properties. We prove that the…

We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplex of classical N-point probability…

The permutation representation afforded by a Coxeter group W acting on the cosets of a standard parabolic subgroup inherits many nice properties from W such as a shellable Bruhat order and a flat deformation over Z[q] to a representation of…

In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we tackle different topics around the field of definition of a hyperbolic…

A selfconsistent definition of quantum free particle on a generic curved manifold emerges naturally by restricting the dynamics to submanifolds of co-dimension one. PACS 0365 0240

We consider compact matrix quantum groups whose $N$-dimensional fundamental representation decomposes into an $(N-1)$-dimensional and a one-dimensional subrepresentation. Even if we know that the compact matrix quantum group associated to…

We define new noncommutative spheres with partial commutation relations for the coordinates. We investigate the quantum groups acting maximally on them, which yields new quantum versions of the orthogonal group: They are partially…

The two-dimensional gauged linear sigma model has provided a physical model for the quantum cohomology of a K\"ahler manifold, $X$. A three-dimensional version of such construction has recently been shown to shed light on models of quantum…

Based on a family of indefinite unitary representations of the diffeomorphism group of an oriented smooth $4$-manifold, a manifestly covariant $4$ dimensional and non-perturbative algebraic quantum field theory formulation of gravity is…

In its most basic form, the finite quantum de Finetti theorem states that the reduced k-partite density operator of an n-partite symmetric state can be approximated by a convex combination of k-fold product states. Variations of this result…

We determine the structure of the cyclotomic Hecke algebra corresponding to the complex reflection group $G_{25}$ also when it is not semisimple, as long as the generators are diagonalizable. In particular, we classify all simple…

We introduce a dimension group for a self-similar map as the ${\rm K}_0$-group of the core of the $C^*$-algebra associated with the self-similar map together with the canonical endomorphism. The key step for the computation is an explicit…

Beginning with a skew-symmetric matrix, we define a certain Poisson--Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or "Lie-Poisson") Poisson bracket. By analyzing this Poisson structure, we gather…

We show that there is no algorithm deciding whether the maximal residually free quotient of a given finitely presented group is finitely presentable or not. Given a finitely generated subgroup G of a finite product of limit groups, we…

We construct the solution $\phi(t,{\bf x})$ of the quantum wave equation $\Box\phi + m^2\phi + \lambda:\!\!\phi^3\!\!: = 0$ as a bilinear form which can be expanded over Wick polynomials of the free $in$-field, and where $:\!\phi^3(t,{\bf…

This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…

We consider a free particle in a de Sitter spacetime. We use a picture in which the analogs of the Schr\"odinger operators of the particle are independent of both the time and the space coordinates. These operators induce operators which…

We propose a definition of a quantum homogeneous space of a locally compact quantum group. We show that classically it reduces to the notion of a homogeneous spaces. On the quantum level our definition goes beyond the quotient case. It…

The Dunkl operators associated to a necessarily finite Coxeter group acting on a Euclidean space are generalized to any finite group using the techniques of non-commutative geometry, as introduced by the authors to view the usual Dunkl…

Various properties of two kinds of massless representations of the n-conformal (or (n+1)-De Sitter) group $\tilde{G}_n=\widetilde{SO}_0(2,n)$ are investigated for $n\ge2$. It is found that, for space-time dimensions $n\ge3$, the situation…