Reading Seminar: Representation theory - The basics

Groups are a fundamental construct to understand “symme- tries”. They are best understood by studying their action on linear vector spaces, that is via linear representations i.e. their concrete realization as matrices. This for example appears in

• harmonic analysis (think: the Fourier transform of periodic functions)
• tensor decomposition (a matrix (a 2-tensor) can be split into a symmetric part and an antisymmetric part; what about higher order tensors?)
• the study of certain Markov chains

This is a reading group of

Fulton, William, and Joe Harris. Representation theory: a first course. Vol. 129. Springer Science & Business Media, 2013.

We will go through Chapter 1-15; at the speed required by the group. Starting essentially from scratch in Chapter 1, at the end we will have a solid understanding of representations of the symmetric group (permutations) and the general linear group (invertible matrices).
Each week one designated “leader” will guide the session, but all attendants are asked to read the relevant chapter before. We will work with examples (by hand and by code) as much as possible.

Date and time info
first lecture: Tuesday 16.10.2018 at 11:00h

Keywords
representation theory; symmetric group; GL

Audience
MSc students, PhD students, Postdocs