New Formulas and Conjectures for the Nabla Operator
Francois Bergeron
TL;DR
This paper introduces new formulas for the nabla operator and explores its impact on Schur functions, providing representation theoretic insights into related conjectures in diagonal harmonics.
Contribution
It presents novel formulas for the nabla operator and offers representation theoretic explanations for conjectures about its action on Schur functions.
Findings
New formulas involving the nabla operator
Representation theoretic explanations for conjectures
Insights into the effect of nabla on Schur functions
Abstract
The operator nabla, introduced by Garsia and the author, plays a crucial role in many aspect of the study of diagonal harmonics. Besides giving several new formulas involving this operator, we show how one is lead to representation theoretic explanations for conjectures about the effect of this operator on Schur functions.
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
TopicsAdvanced Combinatorial Mathematics · Mathematical functions and polynomials · Advanced Mathematical Identities