Exterior differential algebras and flat connections on Weyl groups

Abstract

We study some aspects of noncommutative differential geometry on a finite Weyl group in the sense of S. Woronowicz, K. Bresser {\it et al.}, and S. Majid. For any finite Weyl group $W$ we consider the subalgebra generated by flat connections in the left-invariant exterior differential algebra of $W.$ For root systems of type $A$ and $D$ we describe a set of relations between the flat connections, which conjecturally is a complete set.

References in corpus (5)

• Inhomogeneous lattice paths, generalized Kostka polynomials and A${}_{n-1}$ supernomials
• Character Formulae of ${\widehat{sl}}_n$-Modules and Inhomogeneous Paths
• Residues formulae for volumes and Ehrhart polynomials of convex polytopes
• Geometric Proofs of Horn and Saturation Conjectures
• Noncommutative algebras related with Schubert calculus on Coxeter groups