
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.
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