Homfly-Pt and Alexander polynomials from a doubled Schur algebra

TL;DR

This paper introduces a generalized doubled Schur algebra framework that unifies the quantum group approach to the Homfly-Pt polynomial, Alexander polynomial, and slm Reshetikhin-Turaev invariants.

Contribution

It presents a new algebraic structure that unifies various knot invariants within a single quantum group-based setting.

Findings

Unified algebraic framework for Homfly-Pt, Alexander, and slm invariants

Generalized doubled Schur algebra encapsulates multiple polynomial invariants

Provides a basis for further algebraic and topological studies

Abstract

We define a generalization of the idempotented Schur algebra which gives a unified setting for a quantum group presentation of the Homfly-Pt polynomial, together with its specializations to the Alexander polynomial and the slm Reshetikhin-Turaev invariants.