相关论文: Notes on groups and representations

This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular homogeneous space of non-reductive type, the so…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

In this short note we introduce a new metric on certain finite groups. It leads to a class of groups for which the element orders satisfy an interesting inequality. This extends the class CP_2 studied in our previous paper [16].

Small representations of a group bring us to large symmetries in a representation space. Analysis on minimal representations utilises large symmetries in their geometric models, and serves as a driving force in creating new interesting…

This short note collects three open questions on cut groups (a class of groups generalizing rational groups).

The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the first in a series of papers in…

Here I share a few notes I used in various course lectures, talks, etc. Some may be just calculations that in the textbooks are more complicated, scattered, or less specific; others may be simple observations I found useful or curious.

We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.

These are some basic notes concerning Holder and Lipschitz classes on metric spaces.

The note complements topological aspects of the theory of chiral algebras.

We discuss a connection between two areas of mathematics which until recently seemed to be rather distant from each other: (1) noncommutative harmonic analysis on groups and (2) some topics in probability theory related to random point…

The purpose of this note is to provide an overview of the containment problem for symbolic and ordinary powers of homogeneous ideals, related conjectures and examples. We focus here on ideals with zero dimensional support. This is an area…

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

This paper is the second part of arXiv:0707.1766. We develope harmonic analysis in some categories of filtered abelian groups and vector spaces over the fields R or C. These categories contain as objects local fields and adelic spaces…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

These are the notes from my courses on the arithmetic of quadratic forms.

Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…

These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.

We collect some open problems about minimal presentations of numerical semigroups and, more generally, about defining ideals and free resolutions of their semigroup rings and associated graded rings. We emphasize both long-standing problems…