# On modular group representations associated to SO$(p)_2$-TQFTs

## TL;DR

This paper proves that for odd primes greater than 3, the modular group representations linked to SO(p)_2-TQFTs can be realized over cyclotomic integer rings, with explicit bases and connections to Weil representations.

## Contribution

It establishes the integrality of these representations over cyclotomic integers and provides explicit bases, linking TQFTs to number theory and finite field representations.

## Key findings

- Representations are defined over cyclotomic integer rings.
- Explicit integral bases are constructed.
- Connections to Weil representations over finite fields are established.

## Abstract

In this paper, we prove that for any odd prime larger than 3, the modular group representation associated to the SO$(p)_2$-TQFT can be defined over the ring of integers of a cyclotomic field. We will provide explicit integral bases. In the last section, we will relate these representations to the Weil representations over finite fields.