On a state model for the SO(2n) Kauffman polynomial

TL;DR

This paper develops a new state model for the SO(2n) Kauffman polynomial by applying the MOY framework to Jaeger's link invariant decomposition, enabling recursive evaluation using planar graphs.

Contribution

It introduces a novel state summation model for the SO(2n) Kauffman polynomial based on the MOY approach, extending link invariant computations.

Findings

Constructed a state model for SO(2n) Kauffman polynomial.

Unified MOY framework with Jaeger's link invariant decomposition.

Facilitated recursive evaluation of the polynomial using planar graphs.

Abstract

F. Jaeger presented the two-variable Kauffman polynomial of an unoriented link L as a weighted sum of HOMFLY-PT polynomials of oriented links associated with L. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the sl(n)-link invariant (a one-variable specialization of the HOMFLY-PT polynomial). We apply the MOY framework to Jaeger's work, and construct a state summation model for the SO(2n) Kauffman polynomial.