Related papers: Infinite Permutation Groups
The physics of systems that cannot be described by a Hermitian Hamiltonian, has been attracting a great deal of attention in recent years, motivated by their nontrivial responses and by a plethora of applications for sensing, lasing, energy…
This paper is concerned with integrals which integrands are the monomials of matrix elements of irreducible representations of classical groups. Based on analysis on Young tableaux, we discuss some related duality theorems and compute the…
These notes give a short introduction to finite Coxeter groups, their classification, and some parts of their representation theory, with a focus on the infinite families. They are based on lectures delivered by the author at the…
These lecture notes were prepared for a special topics course in the Department of Statistics at the University of Washington, Seattle. They comprise the first eight chapters of a book currently in progress.
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
Comment on ``The 2005 Neyman Lecture: Dynamic Indeterminism in Science'' [arXiv:0808.0620]
Following my plenary lecture on ICMP2000 I review my results concerning two closely related topics: topological quantum field theories and the problem of quantization of gauge theories. I start with old results (first examples of…
Let S=Sym(\Omega) be the group of all permutations of an infinite set \Omega. Extending an argument of Macpherson and Neumann, it is shown that if U is a generating set for S as a group, respectively as a monoid, then there exists a…
The present notes are based on a course given by J-P.Serre at ENSJF in 1978/79 on the elementary properties of finite groups. They were first written down by M.Buhler and C.Goldstein (Montrouge 1979), then revised and put in LaTeX by…
Lecture notes from the 1994 CRM-CAP Summer School ``Particles and Fields '94''. Covers material written elsewhere in a more leisurely fashion, including many exercises. Describes derivation of quantum groups from the Chern-Simons lagrangian…
These are yet another lecture notes on Seiberg-Witten invariants, where no claim of originality is made, they contain a discussion of some related results from the recent literature.
This is a write-up of the discussions during the meetings of the study group on representation theory of semirings which was organized at the Department of Mathematics, Uppsala University, during the academic year 2017-2018. The main…
We define a new invariant of finitely generated representations of a finite group, with coefficients in a commutative noetherian ring. This invariant uses group cohomology and takes values in the singularity category of the coefficient…
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts…
The finite sharply $2$-transitive groups were classified by Zassenhaus in the 1930's. They essentially all look like the group of affine linear transformations $x\mapsto ax+b$ for some field (or at least near-field) $K$. However, the…
An infinite permutation is a linear ordering of the set of non-negative integers. Generally, the properties of infinite permutations analogous to those of infinite words show some resemblances and some differences between permutations and…
Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold…
Bounded cohomology of groups was first studied by Gromov in 1982. Since then it has sparked much research in Geometric Group Theory. However, it is notoriously hard to explicitly compute bounded cohomology, even for most basic…
This article began as a study of the structure of infinite permutation groups G in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point…
The remarkable technical contributions of Michael E. Fisher to statistical physics and the development of the renormalization group are widely known and deeply influential. But less well-known is his early and profound appreciation of the…