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 Algebra Logika: Year: Volume: Issue: Page: Find

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

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

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
\Bibitem{Bel07} \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 \mathnet{http://mi.mathnet.ru/al6} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2321077} \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} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255037700001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33847665544} 

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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
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
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
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
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
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
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
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
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
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
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
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