相关论文: Equivariant spectral triples on the quantum SU(2) …

In this paper we achieve the quantization of a particle moving on the $SU(2)$ group manifold, that is, the three-dimensional sphere $S^{3}$, by using group-theoretical methods. For this purpose, a fundamental role is played by contact,…

Let $\pi$ be a group equipped with an action of a second group $G$ by automorphisms. We define the equivariant cohomological dimension ${\sf cd}_G(\pi)$, the equivariant geometric dimension ${\sf gd}_G(\pi)$, and the equivariant…

We extend SO(4,2) covariant lightcone embedding methods of four-dimensional CFTs to N=1 superconformal field theory (SCFT). Manifest superconformal SU(2,2|1) invariance is achieved by realizing 4D superconformal space as a surface embedded…

A covariant - tensor method for $SU(2)_{q}$ is described. This tensor method is used to calculate q - deformed Clebsch - Gordan coefficients. The connection with covariant oscillators and irreducible tensor operators is established. This…

The Quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even-even and odd-even nuclei. It manifests itself through a dominance of single-particle and quadrupole-quadrupole terms in the Hamiltonian used to…

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…

We briefly describe our application of a version of noncommutative differential geometry to the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$ and sketch how this might be used to determine the correct physical…

We study the spectral metric aspects of the standard Podles sphere, which is a homogeneous space for quantum SU(2). The point of departure is the real equivariant spectral triple investigated by Dabrowski and Sitarz. The Dirac operator of…

By modifying the ideas from our previous paper [SIGMA 13 (2017), 075, 26 pages, arXiv:1705.04005], we construct spectral triples from implementations of covariant derivations on the quantum disk.

A complete system of differential invariants for equivalence of curves in the $n$-dimensional pseudo-euclidean space with respect to the action of each of the groups $K^n \lhd O(n,p,K)$, $K^n \lhd SO(n,p,K)$, $O(n,p,K)$, and $SO(n,p,K)$,…

This is the third in a series of papers on standard monomial theory and invariant theory of arc spaces. For any algebraically closed field $K$, we prove the arc space analogue of the first and second fundamental theorems of invariant theory…

We compute the equivariant $KO$-homology of the classifying space for proper actions of $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. We also compute the Bredon homology and equivariant $K$-homology of the classifying spaces…

The generalized volume conjecture and the AJ conjecture (a.k.a. the quantum volume conjecture) are extended to $U_q(\fraksl_2)$ colored quantum invariants of the theta and tetrahedron graph. The $\SL(2,\bC)$ character variety of the…

We propose a set of 4 recurrence relations whose linear combination gives the number of group invariants, equivalently the dimension of the invariant subspace, in the tensor product of an arbitrary number of adjoint representations of the…

Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions…

The effective action in four dimensions resulting from the ten-dimensional N=1 heterotic supergravity coupled to N=1 supersymmetric Yang-Mills upon dimensional reduction over nearly-Kaehler manifolds is discussed. Nearly-Kaehler manifolds…

The generalised spectral dimension $D_{ S}(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of…

The quantum group analogue of the normalizer of SU(1,1) in SL(2,C) is an important and non-trivial example of a non-compact quantum group. The general theory of locally compact quantum groups in the operator algebra setting implies the…

A 2-category was introduced in arXiv:0803.3652 [math.QA] that categorifies Lusztig's integral version of quantum sl(2). Here we construct for each positive integer N arepresentation of this 2-category using the equivariant cohomology of…

A proper etale Lie groupoid is modelled as a (noncommutative) spectral geometric space. The spectral triple is built on the algebra of smooth functions on the groupoid base which are invariant under the groupoid action. Stiefel-Whitney…