Weil representations of twisted loop groups of type $A_n^{(2)}$

TL;DR

This paper constructs Weil representations for twisted loop groups of type A_n^{(2)} over local fields and establishes their connection to the two-fold metaplectic cover of the affine Kac-Moody group, advancing understanding of their representation theory.

Contribution

It introduces explicit Weil representations for twisted loop groups of type A_n^{(2)} and links them to known metaplectic covers, providing new insights into their structure.

Findings

Weil representations of twisted loop groups are explicitly constructed.

The associated cover matches the two-fold metaplectic cover of the affine Kac-Moody group.

The work bridges twisted loop groups with established metaplectic structures.

Abstract

We construct Weil representations of twisted loop groups of type $A_n^{(2)}$ over local fields. We prove that the associated cover of the twisted loop group is the two fold metaplectic cover of the affine Kac-Moody group of type $A_n^{(2)}$ given by Patnaik-Puskas.