Geodesic
On the conjecture about semiproportional characters in the groups $\mathrm{Sp}_4(q)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 30-46 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters $\varphi$ and $\psi$, then $\varphi(1)=\psi(1)$. In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for the symplectic groups $\mathrm{Sp}_4(q)$ and $\mathrm{PSp}_4(q)$.
Keywords: finite symplectic groups, character table, semiproportional characters, small interactions. 
@article{TIMM_2012_18_3_a4,
     author = {V. A. Belonogov},
     title = {On the conjecture about semiproportional characters in the groups~$\mathrm{Sp}_4(q)$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {30--46},
     year = {2012},
     volume = {18},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a4/}
}
TY  - JOUR
AU  - V. A. Belonogov
TI  - On the conjecture about semiproportional characters in the groups $\mathrm{Sp}_4(q)$
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2012
SP  - 30
EP  - 46
VL  - 18
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a4/
LA  - ru
ID  - TIMM_2012_18_3_a4
ER  - 
%0 Journal Article
%A V. A. Belonogov
%T On the conjecture about semiproportional characters in the groups $\mathrm{Sp}_4(q)$
%J Trudy Instituta matematiki i mehaniki
%D 2012
%P 30-46
%V 18
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a4/
%G ru
%F TIMM_2012_18_3_a4
V. A. Belonogov. On the conjecture about semiproportional characters in the groups $\mathrm{Sp}_4(q)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 3, pp. 30-46. http://geodesic.mathdoc.fr/item/TIMM_2012_18_3_a4/

[1] Belonogov V. A., Predstavleniya i kharaktery v teorii konechnykh grupp, UrO AN SSSR, Sverdlovsk, 1990, 380 pp. | MR

[2] Belonogov V. A., “Vzaimodeistviya i $D$-bloki v konechnykh gruppakh”, Podgruppovaya struktura grupp, UrO AN SSSR, Sverdlovsk, 1988, 4–44 | MR

[3] Belonogov V. A., “O malykh vzaimodeistviyakh v konechnykh gruppakh”, Tr. In-ta matematiki i mekhaniki UrO RAN, 2, 1992, 3–18 | MR | Zbl

[4] Belonogov V. A., “Malye vzaimodeistviya v gruppakh $\mathrm{GL}_3(q)$, $\mathrm{GU}_3(q)$, $\mathrm{PGL}_3(q)$ i $\mathrm{PGU}_3(q)$”, Tr. In-ta matematiki i mekhaniki UrO RAN, 4, 1996, 17–47 | MR | Zbl

[5] Belonogov V. A., “Malye vzaimodeistviya v gruppakh $\mathrm{SL}_3(q)$, $\mathrm{SU}_3(q)$, $\mathrm{PSL}_3(q)$ i $\mathrm{PSU}_3(q)$”, Tr. In-ta matematiki i mekhaniki UrO RAN, 5, 1998, 3–27 | Zbl

[6] Belonogov V. A., “Malye vzaimodeistviya v gruppakh $\mathrm{Sp}_4(q)$ pri chëtnykh $q$”, Tr. In-ta matematiki i mekhaniki UrO RAN, 17, no. 4, 2011, 19–37

[7] Belonogov V. A., “K gipoteze o poluproportsionalnykh kharakterakh”, Sib. mat. zhurn., 46:2 (2005), 299–314 | MR | Zbl

[8] Srinivasan B., “The characters of the finite symplectic group $\mathrm{Sp}(4,q)$”, Trans. Amer. Math. Soc., 131:2 (1968), 488–525 | MR | Zbl

[9] Przygocki A., “Schur indices of symplectic groups”, Commun. Algebra, 10:3 (1982), 279–310 | DOI | MR | Zbl