Details
| Original language | English |
|---|---|
| Pages (from-to) | 353-369 |
| Number of pages | 17 |
| Journal | Algebraic Combinatorics |
| Volume | 1 |
| Issue number | 3 |
| Early online date | 28 Jun 2018 |
| Publication status | Published - 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.
Keywords
- Characters, Double cover groups, Hook character, Kronecker products, Saxl conjecture, Spin characters, Symmetric groups, Unimodal sequences
ASJC Scopus subject areas
- Mathematics(all)
- Discrete Mathematics and Combinatorics
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In: Algebraic Combinatorics, Vol. 1, No. 3, 2018, p. 353-369.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Critical classes, Kronecker products of spin characters, and the Saxl conjecture
AU - Bessenrodt, Christine
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - Characters
KW - Double cover groups
KW - Hook character
KW - Kronecker products
KW - Saxl conjecture
KW - Spin characters
KW - Symmetric groups
KW - Unimodal sequences
UR - http://www.scopus.com/inward/record.url?scp=85094308710&partnerID=8YFLogxK
U2 - 10.5802/alco.18
DO - 10.5802/alco.18
M3 - Article
AN - SCOPUS:85094308710
VL - 1
SP - 353
EP - 369
JO - Algebraic Combinatorics
JF - Algebraic Combinatorics
IS - 3
ER -