Introduction to Diffusive Representation

Introduction to diffusive representation

Diffusive representation is an operator theory elaborated during the last years. It is devoted to time-nonlocal problems, allowing significant simplifications for analysis and numerical realization of integral time operators encountered in many physical situations. Namely, most of the shortcomings induced by time-nonlocal formulations are by-passed by use of suitable time-local state realizatio...

Introduction to Geometric Representation Theory

These notes are a rough write-up of lectures presented at the workshop on “Geometry and Integrability”, held at the University of Melbourne, 6-15 Feb, 2008. My interest in Geometric Representation Theory stems from recent developments in the Geometric Langlands program. These lectures are an introduction into material which are a prerequisite to anyone interested in studying the Geometric Langl...

An Elementary Introduction to Categorical Representation Theory

In this expository article, we will give a brief introduction to the categorical representation theory, some of which can be found in [8, 9]. The idea of categorification dates back to I. B. Frenkel. He proposed that one can construct a tensor category whose Grothendieck ring is isomorphic to the representation theory of the simplest quantum group Uq(sl2) (see, for example, [6, 7]). Since then,...

Introduction to representation theory of finite groups

An Introduction to Aspect-Oriented Music Representation

The composition of music in many idioms involves the exploitation of recurrent, recombinant musical fragments. Any given fragment may, as a consequence, appear in arbitrarily many structures, in its original or transformed state. Such a fragment is said to crosscut the musical structure, in the sense that the modification of such a fragment implies that revisions should be made to related struc...