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Determining a connected split reductive group from its irreducible representations
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CheeWhye Chin
Published/Copyright:
September 30, 2008
Abstract
We show that a connected split reductive group G over a field of characteristic 0 is 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. More precisely, we determine all isomorphisms compatible with the specified data.
Received: 2007-04-16
Revised: 2007-11-26
Published Online: 2008-09-30
© de Gruyter 2008
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Articles in the same Issue
- Constructive membership in black-box groups
- Connectivity of the product replacement algorithm graph of PSL(2, q)
- A method of Bender applied to groups of J3-type
- Determining a connected split reductive group from its irreducible representations
- A construction of almost all Brauer trees
- Irreducible components and isomorphisms of the Burnside ring
- On the single-orbit conjecture for uncoverings-by-bases
- On 2-generated subgroups and products of groups
- Covering number for reflections in trees
- A formula for the normal subgroup growth of Baumslag–Solitar groups
- Graphs, free groups and the Hanna Neumann conjecture
