The diagram category of framed tangles and invariants of quantized symplectic group

TL;DR

This paper develops a categorical framework for the invariant theory of quantized symplectic groups using braided monoidal categories and framed tangles, providing a new perspective on their invariants.

Contribution

It introduces a categorical version of the fundamental theorems for quantized symplectic groups based on the diagram category of framed tangles.

Findings

Categorical formulation of invariant theory theorems

Application of braided monoidal categories to symplectic groups

New diagrammatic approach to invariants

Abstract

In this paper we present a categorical version of the first and second fundamental theorems of the invariant theory for the quantized symplectic groups. Our methods depend on the theory of braided strict monoidal categories which are pivotal, more explicitly the diagram category of framed tangles.