A note on the gl(m|n) link invariants and the HOMFLY-PT polynomial
Hoel Queffelec, Antonio Sartori
TL;DR
This paper provides a unified representation-theoretical framework for various type A link invariants, including HOMFLY-PT, Jones, Alexander, and gl(m|n) quantum invariants, using the quantized oriented Brauer category.
Contribution
It introduces a novel, unified approach to understanding type A link invariants through the lens of the quantized oriented Brauer category, connecting multiple invariants.
Findings
Unified representation-theoretical treatment of type A invariants
Connection of invariants with the quantized oriented Brauer category
Simplification of understanding relationships among different invariants
Abstract
We present a short and unified representation-theoretical treatment of type A link invariants (that is, the HOMFLY-PT polynomials, the Jones polynomial, the Alexander polynomial and, more generally, the gl(m|n) quantum invariants) as link invariants with values in the quantized oriented Brauer category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Nonlinear Waves and Solitons · Geometric and Algebraic Topology