Jacobi–Trudi formulas and determinantal varieties

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 07 Nov 2023Embargo end date: 01 Jan 2022 Poland English Publisher:MathDoc/Centre MersenneJournal:Algebraic Combinatorics, volume 6, pages 1,163-1,175 (eissn: 2589-5486,

Copyright policy )Funded by:NSF | CAREER: Categorical and ..., NSF | Applications of Represent...

Authors: Sam, Steven V; Weyman, Jerzy;

doi: 10.5802/alco.299 , 10.48550/arxiv.2206.07728

arXiv: 2206.07728

Jacobi–Trudi formulas and determinantal varieties

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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.

Country

Poland

Related Organizations

University of California, San Francisco
United States
Jagiellonian University
Poland
University of Connecticut
United States

Keywords

BGG resolution, Symmetric functions and generalizations, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Jacobi-Trudi identity, Combinatorial aspects of simplicial complexes, Combinatorial aspects of representation theory, FOS: Mathematics, Mathematics - Combinatorics, symmetric functions, Combinatorics (math.CO), Representation Theory (math.RT), Mathematics - Representation Theory

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