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Algebra Logika, 2007, Volume 46, Number 1, Pages 3–25 (Mi al6)  

This article is cited in 11 scientific papers (total in 11 papers)

Irreducible characters with equal roots in the groups $S_n$ and $A_n$

V. A. Belonogov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We show that treating of (non-trivial) pairs of irreducible characters of the group $S_n$ sharing the same set of roots on one of the sets $A_n$ and $S_n\setminus A_n$ is divided into three parts. This, in particular, implies that any pair of such characters $\chi^\alpha$ and $\chi^\beta$ ($\alpha$ and $\beta$ are respective partitions of a number $n$) possesses the following property: lengths $d(\alpha)$ and $d(\beta)$ of principal diagonals of Young diagrams for $\alpha$ and $\beta$ differ by at most 1.

Keywords: group, irreducible character, Young diagram.

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English version:
Algebra and Logic, 2007, 46:1, 1–15

Bibliographic databases:

UDC: 512.54
Received: 02.03.2006

Citation: V. A. Belonogov, “Irreducible characters with equal roots in the groups $S_n$ and $A_n$”, Algebra Logika, 46:1 (2007), 3–25; Algebra and Logic, 46:1 (2007), 1–15

Citation in format AMSBIB
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\by V.~A.~Belonogov
\paper Irreducible characters with equal roots in the groups $S_n$ and~$A_n$
\jour Algebra Logika
\yr 2007
\vol 46
\issue 1
\pages 3--25
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\zmath{https://zbmath.org/?q=an:1156.20010}
\transl
\jour Algebra and Logic
\yr 2007
\vol 46
\issue 1
\pages 1--15
\crossref{https://doi.org/10.1007/s10469-007-0001-7}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. A. Belonogov, “Certain pairs of irreducible characters of the groups $S_n$ and $A_n$”, Proc. Steklov Inst. Math. (Suppl.), 257, suppl. 1 (2007), S10–S46  mathnet  crossref  mathscinet  elib
    2. V. A. Belonogov, “Certain pairs of irreducible characters of the groups $S_n$”, Proc. Steklov Inst. Math. (Suppl.), 259, suppl. 2 (2007), S12–S34  mathnet  crossref  elib
    3. V. A. Belonogov, “Irreducible characters of the group $S_n$ that are semiproportional on $A_n$”, Algebra and Logic, 47:2 (2008), 77–90  mathnet  crossref  mathscinet  zmath  isi
    4. V. A. Belonogov, “The young diagrams of a pair of irreducible characters of $S_n$ with the same zero set on $S^\varepsilon_n$”, Siberian Math. J., 49:5 (2008), 784–795  mathnet  crossref  mathscinet  isi
    5. V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. I”, Proc. Steklov Inst. Math. (Suppl.), 263, suppl. 2 (2008), S150–S171  mathnet  crossref  zmath  isi  elib
    6. 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  mathnet  crossref  mathscinet  isi  elib
    7. 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  mathnet  elib
    8. 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  mathnet  crossref  isi  elib
    9. 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  mathnet  elib
    10. 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  mathnet  crossref  isi  elib
    11. 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  mathnet  elib
  • Алгебра и логика Algebra and Logic
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