Super-easy quantum groups with arbitrary parameters

TL;DR

This paper extends the theory of easy quantum groups by allowing more general Schur-Weyl symbols, providing axiomatization, classification, and analysis of quantum unitary and reflection groups.

Contribution

It introduces a broader formalism for easy quantum groups with generalized Kronecker symbols, including new axioms, structure results, and classifications.

Findings

Extended the formalism to include symbols in rac{ ext{T}}{ ext{0}}

Provided axiomatization and classification results

Analyzed quantum unitary and reflection groups with mixed results

Abstract

We discuss an extended easy quantum group formalism, with the Schur-Weyl theoretic Kronecker symbols being as general as possible, and allowed to take values in $\{-1,0,1\}$, and more generally in $\mathbb T\cup\{0\}$. Our study includes an axiomatization of the theory, some structure and classification results, and the study of the basic examples of quantum unitary and reflection groups, with both positive and negative results.