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Tanisaki witness relations for harmonic differential forms
Swanson, Joshua P.1
1 University of Southern California Department of mathematics Los Angeles CA 90089 (USA)
Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 159-185.

Inspired by a series of conjectures and formulas related to higher coinvariant algebras, we present two families of relations involving harmonic differential forms of the symmetric group. Our relations, together with a novel bijection, are sufficient to give a filtration of the 1-forms suggested by work of Haglund–Rhoades–Shimozono with composition factors given by Tanisaki quotients. These are “almost all” of the necessary relations in a certain asymptotic sense we make precise.

Received:
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DOI: 10.5802/alco.334
Classification: 05E10, 05E16
Keywords: coinvariant algebras, Delta Conjecture, Tanisaki ideals, differential harmonics

Swanson, Joshua P. 1

1 University of Southern California Department of mathematics Los Angeles CA 90089 (USA)
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Swanson, Joshua P. Tanisaki witness relations  for harmonic differential forms. Algebraic Combinatorics, Volume 7 (2024) no. 1, pp. 159-185. doi : 10.5802/alco.334. https://alco.centre-mersenne.org/articles/10.5802/alco.334/

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