Unipotent representations and derived functor modules

1993 ◽  
pp. 225-238
Author(s):  
Dan Barbasch
Keyword(s):  
Derived Functor ◽  
Unipotent Representations

On the unitarizability of derived functor modules

1984 ◽  
Vol 78 (1) ◽  
pp. 131-141 ◽  
Author(s):  
Nolan R. Wallach
Keyword(s):  
Derived Functor

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).

On copure projective and cotorsion modules

2019 ◽  
Vol 56 (1) ◽  
pp. 1-12
Author(s):  
Wei Ren ◽  
Duocai Zhang
Keyword(s):  
Noetherian Rings ◽  
Derived Functor ◽  
Flat Modules

Abstract Let R be an IF ring, or be a ring such that each right R-module has a monomorphic flat envelope and the class of flat modules is coresolving. We firstly give a characterization of copure projective and cotorsion modules by lifting and extension diagrams, which implies that the classes of copure projective and cotorsion modules have some balanced properties. Then, a relative right derived functor is introduced to investigate copure projective and cotorsion dimensions of modules. As applications, some new characterizations of QF rings, perfect rings and noetherian rings are given.

Sign in / Sign up

Export Citation Format

Share Document