ALGEBRAIC COMBINATORICS

no. 4
Splitting Kronecker squares, 2-decomposition numbers, Catalan combinatorics, and the Saxl conjecture
Bessenrodt, Christine; Bowman, Chris1
1 Department of Mathematics University of York Heslington, York, YO10 5DD United Kingdom
Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 863-899.

This paper concerns the symmetric and anti-symmetric Kronecker products of characters of the symmetric groups. We provide new closed formulas for decomposing these products, unexpected connections with 2-modular decomposition numbers, Catalan combinatorics, and a refinement of the famous Saxl conjecture.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.294
Classification: 05A05, 05A10, 05E05, 05A15, 05E10, 05E16, 81Q30
Keywords: Symmetric tensor squares, Kronecker product, symmetric groups, character theory, decomposition numbers, Catalan combinatorics.
Bessenrodt, Christine ; Bowman, Chris 1

1 Department of Mathematics University of York Heslington, York, YO10 5DD United Kingdom
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Bessenrodt, Christine; Bowman, Chris. Splitting Kronecker squares, 2-decomposition numbers, Catalan combinatorics, and the Saxl conjecture. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 863-899. doi : 10.5802/alco.294. https://alco.centre-mersenne.org/articles/10.5802/alco.294/

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