Dept Math & Stat UiT, Forskningsparken B459
  Lecture series: 27.01, 03.02, 10.02 2021 Wed 13:00-14:00

Henrik Winther (Masaryk University Brno, Czech Rep)

Computational Lie Theory

We will discuss applications of symbolic computer algebra to problems in Lie theory and representation theory. In particular I will explain how to represent and solve problems in the two main frameworks for homogeneous geometries, that is the "symbolic calculus in coordinates" framework and the purely algebraic framework coming from the isotropy representation, and how to relate them. In the latter framework, geometrical problems are reduced to pure representation theory.

Therefore we will discuss the most common computational problems in representation theory, including finding invariants, tensor product decomposition, branching problems, and plethysms. Our computer tools will be the DifferentialGeometry package in the program Maple, and the representation theory calculator LiE.

Lectures series is hybrid: in person and via Zoom (to get the link, please contact Boris Kruglikov).