ALGEBRAIC COMBINATORICS

no. 5
Jacobi–Trudi formulas and determinantal varieties
Sam, Steven V1; Weyman, Jerzy2
1 Department of Mathematics, University of California, San Diego, CA USA
2 Department of Mathematics, Jagiellonian University, Kraków, Poland
Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1163-1175.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.299
Classification: 05E05, 05E10
Keywords: symmetric functions, Jacobi-Trudi identity, BGG resolution
Sam, Steven V 1; Weyman, Jerzy 2

1 Department of Mathematics, University of California, San Diego, CA USA
2 Department of Mathematics, Jagiellonian University, Kraków, Poland
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Sam, Steven V; Weyman, Jerzy. Jacobi–Trudi formulas and determinantal varieties. Algebraic Combinatorics, Volume 6 (2023) no. 5, pp. 1163-1175. doi : 10.5802/alco.299. https://alco.centre-mersenne.org/articles/10.5802/alco.299/

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