Representations of adele groups

Automorphic Representations of Adele Groups

Automorphic Representations and L-functions

• Decomposition by central characters • Square-integrable cuspforms • Smoothness of cuspforms • Eigen-cuspforms and automorphic representation • Dirichlet series versus zeta and L-functions • L-functions defined via local data • Factoring unitary representations of adele groups • Spherical representations and Satake parameters • Local data, L-groups, higher L-functions References and historical...

Irreducibility of the tensor product of Albeverio's representations of the Braid groups $B_3$ and $B_4$

‎We consider Albeverio's linear representations of the braid groups $B_3$ and $B_4$‎. ‎We specialize the indeterminates used in defining these representations to non zero complex numbers‎. ‎We then consider the tensor products of the representations of $B_3$ and the tensor products of those of $B_4$‎. ‎We then determine necessary and sufficient conditions that guarantee the irreducibility of th...

2 3 Se p 20 14 PERIODS AND GLOBAL INVARIANTS OF AUTOMORPHIC REPRESENTATIONS

We consider periods of automorphic representations of adele groups defined by integrals along Gelfand subgroups. We define natural maps between local components of such periods and construct corresponding global maps using automorphic L-functions. This leads to an introduction of a global invariant of an automorphic representation arising from two such periods. We compute this invariant in some...

Factorization of unitary representations of adele groups

One disclaimer is necessary: while in principle this factorization result makes it clear that representation theory is relevant to study of automorphic forms and L-functions, in practice there are other things necessary. In effect, one needs to know that the representation theory of reductive linear p-adic groups is tractable, so that conversion of other issues into representation theory is a c...

Groups with Two Extreme Character Degrees and their Minimal Faithful Representations

for a finite group G, we denote by p(G) the minimal degree of faithful permutation representations of G, and denote by c(G), the minimal degree of faithful representation of G by quasi-permutation matrices over the complex field C. In this paper we will assume that, G is a p-group of exponent p and class 2, where p is prime and cd(G) = {1, |G : Z(G)|^1/2}. Then we will s...