Tilting modules and torsion phenomena

TL;DR

This paper constructs new families of quantum group representations over integral domains that interpolate between Weyl and tilting modules, potentially advancing the understanding of character generation in quantum algebra.

Contribution

It introduces interpolating families of modules for quantum groups over $Z[v,v^{-1}]$, bridging Weyl and tilting modules, and explores their role in character theory.

Findings

Families of representations constructed over $Z[v,v^{-1}]$

Potential candidates for objects satisfying Lusztig's character philosophy

Connections to the generation of characters in quantum groups

Abstract

We construct families of representations for quantum groups over $\mathbb{Z}[v,v^{-1}]$-algebras that interpolate between Weyl modules and tilting modules. These families might be candidates for objects with characters satisfying the {\em generations of characters} philosophy of Lusztig and Lusztig-Williamson.