Injectivity of induction in Lie theory
 
 
Description:  Given two isomorphic representations of a simple lie algebra over ℂ induced from two irreducible representations V and W of a parabolic subalgebra, what can be said about V and W? In this talk, we consider the case of the general linear and symplectic Lie algebras. We show that the dominant weights labelling V and W have to coincide up to a Dynkin diagram automorphism. In other terms, induction is injective. The proof relies on a generalised version of the Howe duality, which we will also explain.

This is joint work with J. Guilhot and C. Lecouvey.

Date:  2022-01-26
Start Time:   14:30
Speaker:  Thomas Gerber (EPFL, Lausanne, Switzerland)
Institution:  École Polytechnique Fédérale de Lausanne, Switzerland
Place:  Remote seminar via Zoom: https://videoconf-colibri.zoom.us/j/87906003456?pwd=OEF2QmJKWW91TTNsUFJiOWQ2WjRrdz09
Research Groups: -Algebra and Combinatorics
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