geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
Let be a finite group and a subgroup-inclusion. Then the induced representation in Rep(G) of the 1-dimensional trivial representation is the permutation representation of the coset G-set :
This follows directly as a special case of the general formula for induced representations of finite groups (this Example).
It follows that every virtual permutation representation (hence every element of the representation ring in the image of the canonical morphism from the Burnside ring) is a virtual combination of induced representations of trivial representations.
A generalization of this statement including non-permutation representations is the Brauer induction theorem.
See also
Created on January 28, 2019 at 09:45:40. See the history of this page for a list of all contributions to it.