Jacobi-Trudi formulas and determinantal varieties
Steven V Sam, Jerzy Weyman
TL;DR
This paper explores determinantal formulas related to Schur functions, connecting classical Jacobi-Trudi formulas with Zelevinsky's BGG complexes, and generalizes these formulas to new contexts.
Contribution
It provides a unifying explanation for determinantal formulas of Schur functions using BGG complexes and extends these formulas in novel ways.
Findings
Unified understanding of Jacobi-Trudi and Gessel formulas
Generalizations of determinantal formulas for Schur functions
Connections between combinatorial formulas and algebraic complexes
Abstract
Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi-Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.
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
TopicsMolecular spectroscopy and chirality · Advanced Combinatorial Mathematics · Algebraic structures and combinatorial models