Spinoriality of Orthogonal Representations of GL(n,q)

TL;DR

This paper characterizes when orthogonal representations of GL(n,q) can be lifted to the double cover Pin(V), covering all cases except (3,4), thus advancing understanding of representation lifting in algebraic groups.

Contribution

It provides a complete classification of lifting conditions for orthogonal representations of GL(n,q) across all n and prime powers q, excluding one specific case.

Findings

Identifies all orthogonal representations that lift to Pin(V)

Provides explicit criteria for lifting in most cases

Completes the classification for all (n,q) except (3,4)

Abstract

We determine which orthogonal representations V of GL(n,q) lift to the double cover Pin(V ) of the orthogonal group O(V ). We cover all n and prime powers q, except for (n; q) =(3,4).