Web bases for the general linear groups

TL;DR

This paper constructs a basis for tensor representations of the quantum general linear group, including invariant tensors, advancing understanding of their algebraic structure.

Contribution

It introduces a new basis for tensor products of the quantum general linear group's vector representation and its dual, including invariant subspaces.

Findings

Explicit basis construction for tensor representations

Basis restriction to invariant tensors

Enhanced understanding of quantum group representations

Abstract

Let V be the representation of the quantised enveloping algebra of a general linear group which is the q-analogue of the vector representation. In this paper we construct a basis of the representations obtained by tensoring copies of V and its dual. This basis restricts to a basis of the subspace of invariant tensors.