Related papers: Quantum permutations, Hadamard matrices, and the s…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We survey a research program on the strong convergence of unitary and permutation representations of discrete groups. We also take the opportunity to flesh out details that have not appeared elsewhere.
Lecture notes. Introduction to the cohomology of algebras, Lie algebras, Lie bialgebras and quantum groups. Contains a new derivation of the classification of classical r-matrices in terms of deformation cohomology, and a calculation of the…
We define homological matrices, construct examples of one-dimension restricted homological quantum field theories, and show a relationship between the two theories.
This is an introduction to the finite groups, with focus on the groups of permutations and reflections, and more generally, on the finite groups of unitary matrices. We first discuss the basics of group theory, featuring the cyclic,…
Group field theories are a new type of field theories over group manifolds and a generalization of matrix models, that have recently attracted much interest in quantum gravity research. They represent a development of and a possible link…
The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…
The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…
We introduce the notion of a confluent Vandermonde matrix with quaternion entries and discuss its connection with Lagrange-Hermite interpolation over quaternions. Further results include the formula for the rank of a confluent Vandermonde…
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
The analysis of multiparticle quantum states is a central problem in quantum information processing. This task poses several challenges for experimenters and theoreticians. We give an overview over current problems and possible solutions…
We discuss existence of mixed state of multicomponent system with given spectrum and given reduced density matrices. We give a complete solution of the problem in terms of linear inequalities on the spectra, accompanied with extensive…
In connection with the contribution "Quantum Condensates in Nuclear Matter" some problems are given to become more familiar with the techniques of many-particle physics.
In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…
An exposition of quantum permutation groups where an alternative to the 'Gelfand picture' of compact quantum groups is proposed. This point of view is inspired by algebraic quantum mechanics and posits that states on the algebra of…
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
We introduce two new sets of invariant functions of quark mass matrices, which express the constraints on these mass matrices due to knowledge of the quark mixing matrix. These invariants provide a very simple method to test candidate forms…
We give some very interesting matrices which are orthogonal over groups and, as far as we know, referenced, but in fact undocumented. This note is not intended to be published but available for archival reasons.
The quantum switch is a quantum computational primitive that provides computational advantage by applying operations in a superposition of orders. In particular, it can reduce the number of gate queries required for solving promise problems…