L-indistinguishability for covering groups of algebraic tori

TL;DR

This paper proves that the analogue of a global S-group for Brylinski-Deligne covering groups of algebraic tori is finite, clarifying a key aspect of automorphic representation theory.

Contribution

It establishes the finiteness of the global S-group analogue for Brylinski-Deligne covering groups of tori, advancing understanding of their automorphic representations.

Findings

Finiteness of the global S-group analogue is verified for Brylinski-Deligne covering groups of tori.

Provides new insights into the structure of automorphic representations in covering groups.

Clarifies the relationship between covering groups and their associated S-groups.

Abstract

A global packet may simultaneously contain an automorphic representation and a non-automorphic representation. The global $\mathcal S$-group is expected, and known in some cases, to specify the automorphic representations in each global packet. For a covering group of an algebraic torus, it is not obvious from the definition whether the analogue of a global $\mathcal S$-group has finite order. In this paper, we verify this finiteness for a Brylinski-Deligne covering group of a torus.