相关论文: Projective Group Representations in Quaternionic H…
We study the question of when geometric extension algebras are polynomial quasihereditary. Our main theorem is that under certain assumptions, a geometric extension algebra is polynomial quasihereditary if and only if it arises from an even…
Let $G$ and $T$ be topological groups, $\alpha : T \to \Aut(G)$ a homomorphism defining a continuous action of $T$ on $G$ and $G^\sharp := G \rtimes_\alpha T$ the corresponding semidirect product group. In this paper we address several…
Based on local unitary operators acting on a n-dimensional Hilbert-space, we investigate selective and collective operator basis sets for N-particle quantum networks. Selective cluster operators are used to derive the properties of general…
We establish a regular sampling theory in the range of the analysis operator of a continuous frame having a unitary structure. The unitary structure is related with a unitary representation of a locally compact abelian group on a separable…
Given an explicit presentation of a reflection group of rank two (or any rank two group for that matter), we give a simple procedure for calculating all its systems of imprimitivity, when viewed as a matrix group over the quaternions. This…
In this paper we extend our previous result on the description of the partcle motion in a generalized Heisenberg picture to a relativistic fermion. The operators of the Lorentz algebra in this picture may be regarded as field operators. In…
We describe the K-ring of the classifying space of the generalized quaternion group in terms of generators and the minimal set of relations. We also compute the order of the main generator in the truncated rings.
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation…
Motivated by topological quantum field theory, we investigate the geometric aspects of unitary 2-representations of finite groups on 2-Hilbert spaces, and their 2-characters. We show how the basic ideas of geometric quantization are…
Random sets are used to get a continuous partition of the cardinality of the union of many overlapping sets. The formalism uses M\"obius transforms and adapts Shapley's methodology in cooperative game theory, into the context of set theory.…
In the terms of triples $D^+\to H\to D^-$ of Hilbert spaces we construct an analogue of Friedrichs's extension for operator matrices. Also we establish some general approach to construction of variational principles for such matrices.
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
We construct a class of representations of the Heisenberg algebra in terms of the complex shift operators subject to the proper continuous limit imposed by the correspondence principle. We find a suitable Hilbert space formulation of our…
In the current paper we attempt to transfer the notion of the projectional entropy, originally defined for multidimensional subshifts, to the case of actions of amenable groups. The main theorem states that if a system is strongly…
The paper consists of two parts. The first part introduces the representation ring for the family of compact unitary groups U(1), U(2),.... This novel object is a commutative graded algebra R with infinite-dimensional homogeneous…
We present an explicit construction of a unitary representation of the commutator algebra satisfied by position and momentum operators on the Moyal plane.
Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results…
Antiunitary representations of Lie groups take values in the group of unitary and antiunitary operators on a Hilbert space H. In quantum physics, antiunitary operators implement time inversion or a PCT symmetry, and in the modular theory of…
This is the first in a series of papers on projective positive energy representations of gauge groups. Let $\Xi \rightarrow M$ be a principal fiber bundle, and let $\Gamma_{c}(M,\mathrm{Ad}(\Xi))$ be the group of compactly supported (local)…