A Borel-Weil-Bott type theorem of quantum shuffle algebras

TL;DR

This paper establishes a Borel-Weil-Bott type theorem for the coHochschild homology of quantum shuffle algebras, extending classical geometric results to a non-commutative quantum algebra setting.

Contribution

It introduces a novel theorem linking coHochschild homology of quantum shuffle algebras with non-commutative analogues of line bundles, advancing the understanding of quantum group structures.

Findings

Proves a Borel-Weil-Bott type theorem for quantum shuffle algebras.

Identifies coHochschild homology with non-commutative line bundle analogues.

Extends classical geometric representation theory to quantum algebra context.

Abstract

We prove in this paper a Borel-Weil-Bott type theorem for the coHochschild homology of a quantum shuffle algebra associated with quantum group datum taking coefficients in some well-chosen bicomodules, which can be looked as an analogue of equivariant line bundles over flag varieties in the non-commutative case.