TL;DR
This paper introduces web immanants based on A_2-webs, demonstrating their positivity on totally positive matrices and connecting them to Temperley-Lieb-Martin algebras.
Contribution
It defines web immanants within the A_2-web framework and explores their positivity and algebraic properties, extending prior immanant concepts.
Findings
Web immanants are positive on totally positive matrices.
A new algebraic framework for A_2-webs and their decompositions.
Connections established between web immanants and Temperley-Lieb-Martin algebras.
Abstract
We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg's A_2-webs. We define consistent labelings of webs, and use them to describe the coefficients of decompositions into irreducible webs. We introduce web immanants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices, and describe some further properties.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsWeb Data Mining and Analysis