Unipotent Representations and Unipotent Classes SL(N)

1993 ◽  
Vol 115 (6) ◽  
pp. 1347 ◽  
Author(s):  
Thomas C. Hales
Keyword(s):  
Unipotent Representations

scholarly journals Explicit Hilbert spaces for certain unipotent representations III

2003 ◽  
Vol 201 (2) ◽  
pp. 430-456 ◽  
Author(s):  
Alexander Dvorsky ◽  
Siddhartha Sahi
Keyword(s):  
Hilbert Spaces ◽  
Unipotent Representations

scholarly journals Le Groupe GLn Tordu, Sur un Corps Fini

2006 ◽  
Vol 182 ◽  
pp. 313-379 ◽  
Author(s):  
J.-L. Waldspurger
Keyword(s):  
Irreducible Representation ◽  
Finite Field ◽  
Complex Number ◽  
Outer Automorphism ◽  
The Other ◽  
Characteristic Functions ◽  
Connected Component ◽  
Connected Group ◽  
Unipotent Representations ◽  
Character Sheaves

AbstractLet q be a finite field, G = GLn(q), θ be the outer automorphism of G, suitably normalized. Consider the non-connected group G ⋊ {1, θ} and its connected component = Gθ. We know two ways to produce functions on , with complex values and invariant by conjugation by G: on one hand, let π be an irreducible representation of G we can and do extend to a representation π+ of G ⋊ {1, θ}, then the restriction trace to of the character of π+ is such a function; on the other hand, Lusztig define character-sheaves a, whose characteristic functions ϕ(a) are such functions too. We consider only “quadratic-unipotent” representations. For all such representation π, we define a suitable extension π+, a character-sheave f(π) and we prove an identity trace = γ(π)ϕ(f(π)) with an explicit complex number γ(π).

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