V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 2, 2008, 143–163; Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2008, Volume 14, Number 2, Pages 143–163 (Mi timm31)

This article is cited in 7 scientific papers (total in 7 papers)

Algebra and Topology

On irreducible characters of the group

S_{n}

$S_n$ that are semiproportional on

A_{n}

$A_n$ or

S_{n} ∖ A_{n}

$S_n\setminus A_n$ . I

V. A. Belonogov

Full-text PDF (392 kB) Citations (7)

References:

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Abstract: The hypothesis that the alternating groups

A_{n}

$A_n$ have no pairs of semiproportional irreducible characters is reduced to a hypothesis concerning the problem of describing the pairs of irreducible characters of the symmetric group

S_{n}

$S_n$ that are semiproportional on one of the sets

A_{n}

$A_n$ or

S_{n} ∖ A_{n}

$S_n\setminus A_n$ . The form of this hypothesis (in contrast to the form of the original one) is maximally adapted for an inductive proof. Properties of a pair of the mentioned characters are expressed in terms of the structure of Young's diagrams for these characters. The theorem proved in this paper refines the structure of these diagrams in one of the two possible cases.

Received: 05.02.2007

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2008, Volume 263, Issue 2, Pages S150–S171
DOI: https://doi.org/10.1134/S008154380806014X

Bibliographic databases:

Document Type: Article

UDC: 512.54

Language: Russian

Citation: V. A. Belonogov, “On irreducible characters of the group

S_{n}

$S_n$ that are semiproportional on

A_{n}

$A_n$ or

S_{n} ∖ A_{n}

$S_n\setminus A_n$ . I”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 2, 2008, 143–163; Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150–S171

Citation in format AMSBIB

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\pages 143--163

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\transl

\jour Proc. Steklov Inst. Math. (Suppl.)

\yr 2008

\vol 263

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\pages S150--S171

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Linking options:

https://www.mathnet.ru/eng/timm31

https://www.mathnet.ru/eng/timm/v14/i2/p143

Cycle of papers

On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . I
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2008, 14:2, 143–163
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . II
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2008, 14:3, 58–68
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . III
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2008, 14:4, 12–30
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . IV.
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2009, 15:2, 12–33
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . V
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2010, 16:2, 13–34
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . VI
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2010, 16:3, 25–44
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . VII
V. A. Belonogov
Trudy Inst. Mat. i Mekh. UrO RAN, 2011, 17:1, 3–16

This publication is cited in the following 7 articles:

V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$ , poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$ . VII”, Tr. IMM UrO RAN, 17, no. 1, 2011, 3–16
V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$ , poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$ . V”, Tr. IMM UrO RAN, 16, no. 2, 2010, 13–34
V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . VI”, Proc. Steklov Inst. Math. (Suppl.), 272, suppl. 1 (2011), S14–S35
Belonogov V.A., “On character tables and abstract structure of finite groups”, Character Theory of Finite Groups, Contemporary Mathematics, 524, 2010, 1–10
V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . IV.”, Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S10–S32
V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$ . II”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S60–S71
V. A. Belonogov, “O neprivodimykh kharakterakh gruppy $S_n$ , poluproportsionalnykh na $A_n$ ili na $S_n\setminus A_n$ . III”, Tr. IMM UrO RAN, 14, no. 4, 2008, 12–30

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