Asymptotic values of modular multiplicities for GL_2
Number Theory
2015-09-22 v2 Representation Theory
Abstract
We study the irreducible constituents of the reduction modulo p of irreducible algebraic representations V of Res_{K/Q_p} GL_2 for K a finite extension of Q_p. We show that asymptotically, the multiplicity of each constituent depends only on the dimension of V and the central character of its reduction modulo p. As an application, we compute the asymptotic value of multiplicities that are the object of the Breuil-M\'ezard conjecture.
Keywords
Cite
@article{arxiv.1209.5666,
title = {Asymptotic values of modular multiplicities for GL_2},
author = {Sandra Rozensztajn},
journal= {arXiv preprint arXiv:1209.5666},
year = {2015}
}
Comments
minor changes; to appear in Journal de Th\'eorie des Nombres de Bordeaux