MOY calculus in type D

TL;DR

This paper introduces a new positive state sum for type D webs, leading to a link invariant related to quantum so(2N) modules, connecting diagrammatic calculus with quantum algebraic invariants.

Contribution

It defines a novel positive state sum for type D webs and establishes its relation to Reshetikhin--Turaev invariants for quantum so(2N).

Findings

Defined a positive state sum for type D webs.

Derived a new link invariant from the state sum.

Connected the invariant with existing quantum invariants.

Abstract

We define a positive state sum for webs "of type D". These webs are graphs which mimic morphisms in the category of finite-dimensional quantum so(2N)-modules. From the state sum, we derive an invariant of framed unoriented links. After giving explicit details about some intertwiners in the category of quantum so(2N)-modules, we relate our state-sum link invariant with Reshetikhin--Turaev's invariant associated with quantum so(2N).