Irreducibility Criteria for Local and Global Representations

TL;DR

This paper establishes criteria under which specific modular cusp forms generate irreducible automorphic representations, providing local and global conditions for irreducibility in algebraic groups.

Contribution

It introduces new irreducibility criteria for automorphic representations generated by modular cusp forms, including local archimedean and non-archimedean cases.

Findings

Certain modular cusp forms generate irreducible automorphic representations

Provides local archimedean and non-archimedean irreducibility criteria

Advances understanding of automorphic representation structure

Abstract

It is proved that certain types of modular cusp forms generate irreducible automorphic representation of the underlying algebraic group. Analogous archimedean and non-archimedean local statements are also given.