The concept of symmetries naturally arises in various areas of mathematics and science, including geometry, number theory, differential equations, and quantum mechanics. The more symmetries an object possesses, the better we can understand it through group-theoretic approaches.Branching problems investigate how large symmetries break down into smaller ones, such as fusion rules, using mathematical formulations based on the language of representations and their restrictions. These problems have been studied for over 80 years. In recent years, there has been a surge of research focused on the restriction of continuous symmetries in infinite-dimensional cases, leading to the development of new geometric and analytic methods.
In my three lectures, I plan to provide an introduction to the branching problems of infinite-dimensional representations of real reductive groups, such as $GL(n, \mathbb{R})$, using plenty of elementary examples to make the basic concepts and key ideas more accessible.
[ timetable ]
The thematic trimester "Representation Theory and Noncommutative Geometry", IHP, Paris, France
Organizers: Alexandre Afgoustidis, Anne-Marie Aubert, Pierre Clare, Haluk Şengün.
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© Toshiyuki Kobayashi