The dihedral Dunkl--Dirac symmetry algebra with negative Clifford signature

TL;DR

This paper extends the study of the Dunkl--Dirac symmetry algebra to cases where the Clifford algebra has negative signature, providing foundational results for future representation analysis.

Contribution

It introduces the necessary theoretical framework to analyze Dunkl--Dirac symmetry algebras with negative Clifford signature, building on previous work with positive signature.

Findings

Established foundational results for negative Clifford signature cases

Extended the algebraic framework to new signature settings

Laid groundwork for future representation classification

Abstract

The Dunkl--Dirac symmetry algebra is an associative subalgebra of the tensor product of a Clifford algebra and the faithful polynomial representation of a rational Cherednik algebra. In previous work, the finite-dimensional representations of the Dunkl--Dirac symmetry algebra in three dimensions linked with a dihedral group were given. We give here the necessary results to proceed to the same construction when the Clifford algebra in the tensor product has negative signature.