# Principal series for general linear groups over finite commutative rings

## TL;DR

This paper constructs a family of representations for the general linear group over any finite commutative ring, extending the principal series concept beyond finite fields.

## Contribution

It introduces a new class of representations for $ ext{GL}_n(R)$ over finite commutative rings, generalizing principal series representations from finite fields.

## Key findings

- Representations mirror intertwining properties of classical principal series.
- Extension of principal series to general finite commutative rings.
- Framework applicable to a broad class of rings.

## Abstract

We construct, for any finite commutative ring $R$, a family of representations of the general linear group $\mathrm{GL}_n(R)$ whose intertwining properties mirror those of the principal series for $\mathrm{GL}_n$ over a finite field.