Results 11 to 20 of about 170 (146)

Invariant triple products

International Journal of Mathematics and Mathematical Sciences, 2006
It is shown that the space of invariant trilinear forms on smooth representations of a semisimple Lie group is finite dimensional if the group is a product of hyperbolic groups.
Anton Deitmar
doaj   +1 more source

ENDOSCOPY AND COHOMOLOGY IN A TOWER OF CONGRUENCE MANIFOLDS FOR $U(n,1)$

Forum of Mathematics, Sigma, 2019
By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White, we bound the growth of cohomology in congruence towers of locally ...
SIMON MARSHALL, SUG WOO SHIN
doaj   +1 more source

Representation stability and outer automorphism groups

Documenta Mathematica, 2022
In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups \mathcal{U} . We encode this large amount of data into a convenient abelian category which generalizes the category of VI ...
Pol, Luca, Strickland, Neil Patrick
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Rational structures on automorphic representations [PDF]

Mathematische Annalen, 2017
This paper proves the existence of global rational structures on spaces of cusp forms of general reductive groups. We identify cases where the constructed rational structures are optimal, which includes the case of GL($n$). As an application, we deduce the existence of a natural set of periods attached to cuspidal automorphic representations of GL($n$).
openaire   +4 more sources

A Representation Theorem for the Lorentz Cone Automorphisms

Journal of Optimization Theory and Applications, 2022
In this note we prove a representation theorem for the symmetric cone automorphisms in the spin algebra\, $\Ln$.
openaire   +3 more sources

A Quantization Procedure of Fields Based on Geometric Langlands Correspondence

International Journal of Mathematics and Mathematical Sciences, 2009
We expose a new procedure of quantization of fields, based on the Geometric Langlands Correspondence. Starting from fields in the target space, we first reduce them to the case of fields on one-complex-variable target space, at the same time increasing ...
Do Ngoc Diep
doaj   +1 more source

The Ramanujan and Sato–Tate Conjectures for Bianchi modular forms

Forum of Mathematics, Pi
We prove the Ramanujan and Sato–Tate conjectures for Bianchi modular forms of weight at least $2$ . More generally, we prove these conjectures for all regular algebraic cuspidal automorphic representations of $\operatorname {\mathrm {GL}}_2 ...
George Boxer, Frank Calegari, Toby Gee, James Newton, Jack A. Thorne   +4 more
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On exotic matrix exponential sums and Bessel–Speh functions

Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.
Abstract In a previous work with Carmon, we defined Bessel–Speh functions. These are matrix coefficients of irreducible Speh representations of GLkc(F)$\mathrm{GL}_{kc}(\mathbb {F})$, where F$\mathbb {F}$ is a finite field. They arise from (k,c)$(k,c)$ models, which are models that generalize the Whittaker model to Speh representations attached to ...
Elad Zelingher
wiley   +1 more source

On the Lang–Trotter conjecture for Siegel modular forms

Mathematika, Volume 72, Issue 3, July 2026.
Abstract Let f$f$ be a genus‐two cuspidal Siegel eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated with f$f$, generalizing the results of Ribet and Momose for elliptic modular forms. Using this result, we investigate the distribution of the Hecke eigenvalues ap$a_p$ of f$f$, and obtain upper
Arvind Kumar, Moni Kumari, Ariel Weiss
wiley   +1 more source

Primitivity testing in free group algebras via duality

Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.
Abstract Let K$K$ be a field and F$F$ a free group. By a classical result of Cohn and Lewin, the free group algebra KF$K\left[F\right]$ is a free ideal ring (FIR): a ring over which the submodules of free modules are themselves free, and of a well‐defined rank. Given a finitely generated right ideal I⩽KF$I\leqslant K\left[F\right]$ and an element f∈I$f\
Matan Seidel, Danielle Ernst‐West, Doron Puder   +2 more
wiley   +1 more source