Determining a connected split reductive group from its irreducible representations

2002/11/12 by CheeWhye Chin, Chin, CheeWhye
Materials Science · Mathematics · #Graph theory and applications #Lanthanide and Transition Metal Complexes #math.AG #math.CO #math.RT #msc:20G15

paper · pdf · doi:10.48550/arxiv.math/0211182

11 pages, LaTeX

arxiv created 2007/03/01 · arxiv updated 2009/11/30

Abstract

We show that a connected split reductive group G over a field of characteristic 0 is uniquely determined up to isomorphism by specifying a maximal torus T of G, the set of isomorphism classes of irreducible representations of G, and the character homomorphism from the Grothendieck ring of G to that of T.

Cited by

• Independence of ℓ of monodromy groups

Related

• Representation theory of disconnected reductive groups
• An inverse Satake isomorphism in characteristic p
• Disconnected Reductive Groups: Classification and Representations
• Generic representations for symmetric spaces
• Non-separability and complete reducibility: E_n examples with an application to a question of Külshammer