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31.
32.
V. A. Belonogov 《Algebra and Logic》2007,46(1):1-15
We show that treating of (non-trivial) pairs of irreducible characters of the group Sn sharing the same set of roots on one of the sets An and Sn \ An is divided into three parts. This, in particular, implies that any pair of such characters χα and χβ (α and β are respective partitions of a number n) possesses the following property: lengths d(α) and d(β) of principal diagonals
of Young diagrams for α and β differ by at most 1.
Supported by RFBR grant No. 04-01-00463 and by RFBR-NSFC grant No. 05-01-39000.
__________
Translated from Algebra i Logika, Vol. 46, No. 1, pp. 3–25, January–February, 2007. 相似文献
33.
V. A. Belonogov 《Siberian Mathematical Journal》2008,49(5):784-795
In studying the pairs of irreducible characters of the symmetric group S
n
with the same zero set on A
n
or S
n
∖ A
n
(as well as the pairs of irreducible characters with the same zero set on the alternating group A
n
), the results are important on the connection between the Young diagrams of the characters of these pairs. We prove a theorem
that considerably generalizes two previous results of frequent use in this direction.
Original Russian Text Copyright ? 2008 Belonogov V. A.
The author was supported by the Russian Foundation for Basic Research (Grant 07-01-00148) and the RFBR-NSFC (Grant 05-01-39000).
__________
Ekaterinburg. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 5, pp. 992–1006, September–October, 2008. 相似文献
34.
V. A. Belonogov 《Journal of Mathematical Sciences》2010,167(6):741-748
The results of this paper are connected with one of the main problems of the representation theory, the problem of dependence
between the character table of a finite group and its abstract structure. Finite groups that have a D-block of cardinality 3 for some normal subset D are investigated. Some properties of classical p-blocks (where p is a prime number) consisting of three irreducible characters are also obtained. 相似文献
35.
V. A. Belonogov 《Algebra and Logic》2008,47(2):77-90
Previously, we dubbed the conjecture that the alternating group An has no semiproportional irreducible characters for any natural n [1]. This conjecture was then shown to be equivalent to
the following [3]. Let α and β be partitions of a number n such that their corresponding characters χα and χβ in the group Sn are semiproportional on An. Then one of the partitions α or β is self-associated. Here, we describe all pairs (α, β) of partitions satisfying the hypothesis
and the conclusion of the latter conjecture.
Supported by RFBR (grant No. 07-01-00148) and by RFBR-NSFC (grant No. 05-01-39000).
__________
Translated from Algebra i Logika, Vol. 47, No. 2, pp. 135–156, March–April, 2008. 相似文献
36.
37.
38.
S. E. Demyanov E. Yu. Kaniukov A. V. Petrov E. K. Belonogov E. A. Streltsov D. K. Ivanov Yu. A. Ivanova C. Trautmann H. Terryn M. Petrova J. Ustarroz V. Sivakov 《Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques》2014,8(4):805-813
Si/SiO2/Ni nanostructures are fabricated by the irradiation of an oxidized Si surface with swift heavy ions, nanopore etching in the SiO2 layer, and the electrochemical deposition of nickel in the nanopores with their partial (~50%) or complete filling. Studies of the morphology of the metal in the nanopores shows that the nickel-cluster structure is rather homogeneous and formed by crystallites ~30–50 nm in size. The effects of deposition modes and structure morphology on current transport are analyzed with the use of test temperature dependences of the magnetoresistance. The reproducibility and stability of the magnetoresistance values for the case of homogeneous structure and pore filling with nickel make the Si/SiO2/Ni system promising for application as the base element for high-sensitivity low-temperature magnetic field sensors. 相似文献
39.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):6-23
Previously, the author made the following conjecture: if a finite group has two semiproportional irreducible characters φ and ψ, then φ(1) = ψ(1). In the present paper, a new confirmation of the conjecture is obtained. Namely, the conjecture is verified for symplectic groups Sp4(q) and PSp4(q). 相似文献
40.
V. A. Belonogov 《Proceedings of the Steklov Institute of Mathematics》2009,264(Z1):60-71
In the author’s previous paper, the hypothesis that the alternating groups 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
that are semiproportional on one of the sets A
n
or S
n
∖A
n
. In this hypothesis, properties of such a pair of characters are expressed in terms of Young’s diagrams corresponding to
these characters. The theorem proved in this paper allows one to exclude from consideration some stages of the verification
of this hypothesis. 相似文献