ALGEBRAIC COMBINATORICS

no. 6
Universal characters twisted by roots of unity
Albion, Seamus P.1
1 Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 A-1090 Wien Austria
Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1653-1676.

A classical result of Littlewood gives a factorisation for the Schur function at a set of variables “twisted” by a primitive t-th root of unity, characterised by the core and quotient of the indexing partition. While somewhat neglected, it has proved to be an important tool in the character theory of the symmetric group, the cyclic sieving phenomenon, plethysms of symmetric functions and more. Recently, similar factorisations for the characters of the groups O(2n,ℂ), Sp(2n,ℂ) and SO(2n+1,ℂ) were obtained by Ayyer and Kumari. We lift these results to the level of universal characters, which has the benefit of making the proofs simpler and the structure of the factorisations more transparent. Our approach also allows for universal character extensions of some factorisations of a different nature originally discovered by Ciucu and Krattenthaler, and generalised by Ayyer and Behrend.

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Accepted:
Published online:
DOI: 10.5802/alco.320
Classification: 15A15, 20C15, 05E05, 05E10
Keywords: Schur functions, symplectic characters, orthogonal characters, universal characters, $t$-core, $t$-quotient
Albion, Seamus P. 1

1 Fakultät für Mathematik Universität Wien Oskar-Morgenstern-Platz 1 A-1090 Wien Austria
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Albion, Seamus P. Universal characters  twisted by roots of unity. Algebraic Combinatorics, Volume 6 (2023) no. 6, pp. 1653-1676. doi : 10.5802/alco.320. https://alco.centre-mersenne.org/articles/10.5802/alco.320/

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