Ein Neuer Beweis der Nakayama-Vermutung Über die Blockstruktur Symmetrischer Gruppen

Meier, Nils; Tappe, Jürgen

doi:10.1112/blms/8.1.34

Cited by 12 publications

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“…3 corresponds to the set of /^-numbers 0, 1, 2, 3, 5, 9 , 11, 13, 17. These are /J-numbers for a diagram having first column hook lengths 1,5,7,9,13; that is, for [9,6,5,4,1].…”

Section: -2 Removing a Skew Q-hook Is Equivalent To Decreasing A Fimentioning

confidence: 99%

Some combinatorial results involving Young diagrams

James

1978

Math. Proc. Camb. Phil. Soc.

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1. Introduction. In the first half of this paper we introduce a new method of examining the g-hook structure of a Young diagram, and use it to prove most of the standard results about -power diagram, which is closely connected with the ^-quotient. This concept is interesting because when p is prime a condition involving the p-power diagram appears to be a necessary and sufficient criterion for the diagram to be ^-regular and the corresponding ordinary irreducible representation of @ n to remain irreducible modulo p. In this paper we derive combinatorial results involving the ^>-power diagram, and in a later article we investigate the relevant representation theory.

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“…3 corresponds to the set of /^-numbers 0, 1, 2, 3, 5, 9 , 11, 13, 17. These are /J-numbers for a diagram having first column hook lengths 1,5,7,9,13; that is, for [9,6,5,4,1].…”

Section: -2 Removing a Skew Q-hook Is Equivalent To Decreasing A Fimentioning

confidence: 99%

Some combinatorial results involving Young diagrams

James

1978

Math. Proc. Camb. Phil. Soc.

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“…Section 3 contains prerequisites for the proof of the main result which is then given in Section 4. The outline of the proof is similar to that given in [5] by Meier and Tappe for the linear case, but the details are quite different in the projective case.…”

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confidence: 90%

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confidence: 91%

Blocks of projective representations of the symmetric groups

Humphreys¹

1987

Proceedings of Symposia in Pure Mathematics

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In 1940, Nakayama conjectured that the assignment of irreducible linear representations of the symmetric groups into /^-blocks could be achieved by determining the/>-cores of the Young diagrams associated with the representations. Several proofs of this result are known (see [5]). In [6], Morris conjectured that, at least for odd primes p, a similar result should hold using the p-b&r core to assign irreducible projective representations of the symmetric group into /^-blocks. The purpose of this paper is to establish this conjecture of Morris. The precise formulation of the main theorem is given in Section 1, which also includes an alternative construction of a core diagram due to Macdonald. The equivalence of the two formulations of the conjecture is established in Section 2. Section 3 contains prerequisites for the proof of the main result which is then given in Section 4. The outline of the proof is similar to that given in [5] by Meier and Tappe for the linear case, but the details are quite different in the projective case.

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“…Nakayama's conjecture was proved in 1947 by Brauer and Robinson [1]. Since then, several different proofs have been published, the shortest of which is probably that given in the paper by Meier and Tappe [3].…”

Section: Introductionmentioning

confidence: 99%

“…In the previous section we generalized equation (2) to get formula (3). In this section we will make further generalizations.…”

Section: The Murnaghan-nakayama Rulementioning

confidence: 99%