On mixed products of complex characters of the double covers of the symmetric groups

Bessenrodt, Christine

doi:10.2140/pjm.2001.199.257

Cited by 10 publications

(29 citation statements)

References 12 publications

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“…Similar results for symmetric and alternating groups in arbitrary characteristic or Schur's double covers in characteristic 0 were obtained in [4,5,6,3,13] …”

Section: Theorem C Letsupporting

confidence: 78%

“…Lemma 7.1. Let p > 3, n ≥ 6, and C be the elementary abelian subgroup of order 8 in S n generated by the transpositions (1, 4), (2,5), and (3,6). Set…”

Section: Arbitrary Subgroups (Theorem D)mentioning

confidence: 99%

“…We will write c y forĉyĉ −1 , c ∈ S n , y ∈ FŜ n . By conjugating with t 1 t 2 t 4 t 5 , we note that the elements c (t 1 t 2 )t 1 t 2 are conjugate to each other for c ∈ { (14), (2,5), (3,6)} and c ∈ {(1, 4)(2, 5), (1, 4)(3, 6), (2, 5)(3, 6)}. To identify the corresponding conjugacy classes it suffices to show, using relations, that (i) t 2 t 1 is the lift of (1, 3, 2) ∈ S 6 of order 3; (ii) t 2 t 1 t 1 t 2 = 1;…”

Section: Arbitrary Subgroups (Theorem D)mentioning

confidence: 99%

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On restrictions of modular spin representations of symmetric and alternating groups

Kleshchev

Tiep

2003

Trans. Amer. Math. Soc.

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Abstract. Let F be an algebraically closed field of characteristic p and H be an almost simple group or a central extension of an almost simple group. An important problem in representation theory is to classify the subgroups G of H and FH-modules V such that the restriction V ↓ G is irreducible. For example, this problem is a natural part of the program of describing maximal subgroups in finite classical groups. In this paper we investigate the case of the problem where H is the Schur's double coverÂn orŜn.

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“…Similar results for symmetric and alternating groups in arbitrary characteristic or Schur's double covers in characteristic 0 were obtained in [4,5,6,3,13] …”

Section: Theorem C Letsupporting

confidence: 78%

“…Lemma 7.1. Let p > 3, n ≥ 6, and C be the elementary abelian subgroup of order 8 in S n generated by the transpositions (1, 4), (2,5), and (3,6). Set…”

Section: Arbitrary Subgroups (Theorem D)mentioning

confidence: 99%

Section: Arbitrary Subgroups (Theorem D)mentioning

confidence: 99%

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On restrictions of modular spin representations of symmetric and alternating groups

Kleshchev

Tiep

2003

Trans. Amer. Math. Soc.

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“…(v) While the situations above are the ones used in the later sections, it should be noted that there many more such instances, and we mention just a few examples. For G = GL (3,2), the pair of classes of elements of order 7 is detecting for the pair of characters of degree 3. For G = PSL (2,11), the pair of classes of elements of order 5 (order 11, resp.)…”

Section: Preliminariesmentioning

confidence: 99%

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

Bessenrodt¹

2018

Algebraic Combinatorics

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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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“…A rectangular hull result for spin products was proved in [3], and this was then applied to classify the homogeneous spin products. Also, irreducible mixed products have been determined in [4]. Some information on constituents of small depth in square-like spin products was given in [11].…”

Section: Introductionmentioning

confidence: 99%

On the Durfee size of Kronecker products of characters of the symmetric group and its double covers

Bessenrodt

Behns

2004

Journal of Algebra

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On mixed products of complex characters of the double covers of the symmetric groups

Cited by 10 publications

References 12 publications

On restrictions of modular spin representations of symmetric and alternating groups

On restrictions of modular spin representations of symmetric and alternating groups

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

On the Durfee size of Kronecker products of characters of the symmetric group and its double covers

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