The ring of twisted tilting modules of quantum $GL_n$

TL;DR

This paper introduces the ring of twisted tilting modules for quantum $GL_n$, providing generators, relations, and structural properties, with explicit results for the case of quantum $GL_2$ over a field of characteristic p.

Contribution

It defines the ring of twisted tilting modules for quantum $GL_n$ and explicitly describes its structure for $GL_2$, including generators, relations, and reduction properties.

Findings

The ring of twisted tilting modules is explicitly described for quantum $GL_2$.

The ring is shown to be a reduced ring.

Generators and relations for the ring are provided.

Abstract

Let $G$ be the quantum $GL_n$ over a field of characteristic $p\neq 0$. In this paper we define the ring of twisted tilting modules of $G$. We give generators and relations for the ring of twisted tilting modules of quantum $GL_2(k)$. We also show that this is a reduced ring