Critical classes, Kronecker products of spin characters, and the Saxl conjecture

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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  • Christine Bessenrodt
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OriginalspracheEnglisch
Seiten (von - bis)353-369
Seitenumfang17
FachzeitschriftAlgebraic Combinatorics
Jahrgang1
Ausgabenummer3
Frühes Online-Datum28 Juni 2018
PublikationsstatusVeröffentlicht - 2018

Abstract

Using critical conjugacy classes, we find a new criterion for constituents in Kronecker products of spin characters of the double covers of the symmetric and alternating groups. This is applied together with earlier results on spin characters to obtain constituents in Kronecker products of characters of the symmetric groups. Via this tool, we make progress on the Saxl conjecture; this claims that for a triangular number n, the square of the irreducible character of the symmetric group Sn labelled by the staircase contains all irreducible characters of Sn as constituents. With the new criterion we deduce a large number of constituents in this square which were not detected by other methods, notably all double-hooks. The investigation of Kronecker products of spin characters also inspires a spin variant of Saxl's conjecture.

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Critical classes, Kronecker products of spin characters, and the Saxl conjecture. / Bessenrodt, Christine.
in: Algebraic Combinatorics, Jahrgang 1, Nr. 3, 2018, S. 353-369.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Bessenrodt, C 2018, 'Critical classes, Kronecker products of spin characters, and the Saxl conjecture', Algebraic Combinatorics, Jg. 1, Nr. 3, S. 353-369. https://doi.org/10.5802/alco.18
Bessenrodt C. Critical classes, Kronecker products of spin characters, and the Saxl conjecture. Algebraic Combinatorics. 2018;1(3):353-369. Epub 2018 Jun 28. doi: 10.5802/alco.18
Bessenrodt, Christine. / Critical classes, Kronecker products of spin characters, and the Saxl conjecture. in: Algebraic Combinatorics. 2018 ; Jahrgang 1, Nr. 3. S. 353-369.
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