|
Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 2, Pages 12–33
(Mi timm219)
|
|
|
|
This article is cited in 3 scientific papers (total in 3 papers)
On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. IV.
V. A. Belonogov Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Abstract:
Investigations are continued concerning the conjecture that the alternating groups $A_n$ have no pairs of semiproportional irreducible characters. In order to prove this conjecture by induction on $n$, the author
proposed a new conjecture, formulated in terms of pairs $\chi^\alpha$ and $\chi^\beta$ of irreducible characters of the symmetric group $S_n$ that are semiproportional on one of the sets $A_n$ or $S_n\setminus A_n$ ($\alpha$ and $\beta$ are partitions of the number $n$ corresponding to these characters). The theorem proved in this paper allows one to exclude from consideration the item of this conjecture in which the 4-kernels of the partitions $\alpha$ and $\beta$ have type $3^k.\Sigma_l$.
Keywords:
symmetric groups, alternating groups, irreducible characters, semiproportionality.
Received: 05.12.2008
Citation:
V. A. Belonogov, “On irreducible characters of the group $S_n$ that are semiproportional on $A_n$ or $S_n\setminus A_n$. IV.”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 2, 2009, 12–33; Proc. Steklov Inst. Math. (Suppl.), 267, suppl. 1 (2009), S10–S32
Linking options:
https://www.mathnet.ru/eng/timm219 https://www.mathnet.ru/eng/timm/v15/i2/p12
|
Statistics & downloads: |
Abstract page: | 371 | Full-text PDF : | 68 | References: | 55 | First page: | 1 |
|