Related papers: Quantum Groups and Bounded Symmetric Domains
We establish new upper bounds about symmetric bilinear complexity in any extension of finite fields. Note that these bounds are not asymptotical but uniform. Moreover we give examples of Shimura curves that do not descend over their field…
In this article we give an overview of the Plancherel theory for Riemannian symmetric spaces Z = G/K. In particular we illustrate recently developed methods in Plancherel theory for real spherical spaces by explicating them for Riemannian…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
This is the second part of the paper. Results of the first part about crossed modules are applied here to study of quantum groups in braided categories. Correct cross product in the class of quantum braided groups is built. Criterion when…
In this paper we classify the irreducible Harish-Chandra bimodules with full support over filtered quantizations of conical symplectic singularities under the condition that none of the slices to codimension 2 symplectic leaves has type…
We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametrices and thus can be used to define spectral triples.
Superconducting quantum devices provide excellent connectivity and controllability while semiconductor spin qubits stand out with their long-lasting quantum coherence, fast control, and potential for miniaturization and scaling. In the last…
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
We define and study quantum permutations of infinite sets. This leads to discrete quantum groups which can be viewed as infinite variants of the quantum permutation groups introduced by Wang. More precisely, the resulting quantum groups…
This paper is a detailed study of finite-dimensional modules defined on bicomplex numbers. A number of results are proved on bicomplex square matrices, linear operators, orthogonal bases, self-adjoint operators and Hilbert spaces, including…
The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other classes of bundles as well, including…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among those domains, the quantum matrix ball, was started in…
A new type of local-check additive quantum code is presented. Qubits are associated with edges of a 2-dimensional lattice whereas the stabilizer operators correspond to the faces and the vertices. The boundary of the lattice consists of…
We examine from an algebraic point of view some families of unitary group representations that arise in mathematical physics and are associated to contraction families of Lie groups. The contraction families of groups relate different real…
We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
The spherical wave functions of charge-dyon bounded system in a rectangular spherical quantum dot of infinitely and finite height are calculated. The transcendent equations, defining the energy spectra of the systems are obtained. The…
The results, different aspects and applications of our method of quantisation on configuration manifolds - called Borel Quantisation - were presented at meetings of the series `Symmetries in Science' and can be found in the published…
We survey results in lattice quantum chromodynamics from groups in the USQCD Collaboration. The main focus is on physics, but many aspects of the discussion are aimed at an audience of computational physicists.