Asymptotics for cuspidal representations by functoriality from GL(2)

ON l-ADIC FAMILIES OF CUSPIDAL REPRESENTATIONS OF GL2(Qp)

We compute the universal deformations of cuspidal representations π of GL2(F ) over Fl, where F is a local field of residue characteristic p and l is an odd prime different from p. When π is supercuspidal there is an irreducible, two dimensional representation ρ of GF that corresponds to π via the mod l local Langlands correspondence of [Vi2]; we show that there is a natural isomorphism between...

IRREDUCIBLE REPRESENTATIONS OF GL2(Fq)

The group G = GL2(Fq) is not only the slightly overweight cousin of GL2(C) (it is a “Flabby” S2) but also a tremendously interesting finite group. It is both the automorphism group of the vector space of dimension 2 over the field Fq and a finite group of order q(q − 1)(q − 1), so naturally, representation theorists would like very much to understand its representations. We follow the expositio...

Extensions for supersingular representations of GL2(Qp)

Functoriality for the Exterior Square of Gl4 and the Symmetric Fourth of Gl2

Let ∧ : GLn(C) −→ GLN (C), where N = n(n−1) 2 , be the map given by the exterior square. Then Langlands’ functoriality predicts that there is a map from cuspidal representations of GLn to automorphic representations of GLN , which satisfies certain canonical properties. To explain, let F be a number field, and let A be its ring of adeles. Let π = ⊗ v πv be a cuspidal (automorphic) representatio...

Irreducible cuspidal representations with prescribed local behavior

Let G be a simple algebraic group defined over the global field k. In this paper, we use the simple trace formula to determine the sum of the multiplicities of the irreducible representations in the cuspidal spectrum of G, with specified local behavior at a finite set of places of k and unramified elsewhere. This sum is expressed as the product of the values of modified Artin L-functions at neg...