For citation:
Shulezhko O. V. New Properties of Almost Nilpotent Variety of Exponent 2. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 3, pp. 316-320. DOI: 10.18500/1816-9791-2014-14-3-316-320, EDN: SMSJWZ
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
10.09.2014
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Language:
Russian
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UDC:
512.5
EDN:
SMSJWZ
New Properties of Almost Nilpotent Variety of Exponent 2
Autors:
Shulezhko Olesya Vladimirovna, Ulyanovsk State University
Abstract:
In the presented work we consider numerical characteristics of almost nilpotent variety of exponent 2, which was first constructing in article [1]. The main result of this paper is introduce the exact values of the multiplicities of the irreducible modules appearing in the expansion of the multilinear part of the variety. Meanwhile, we obtain as a consequence the formulas of codimension and colength of the variety of exponent 2.
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References:
- Mishchenko S., Valenti A. An almost nilpotent variety of exponent 2. Israel J. of Math., 2014, vol. 199, iss. 1, pp. 241–257.
- Giambruno A., Zaicev M. Polynomial Identities and Asymptotic Methods. Math. Surv. and Monographs, vol. 122, Providence, RI, Amer. Math. Soc., 2005, 352 p.
- Zaitsev M. V., Mishchenko S. P. Colength of varieties of linear algebras. Math. Notes, 2006, vol. 79, no. 4, pp. 511–517. DOI: 10.1007/s11006-006-0056-0.
- James G. D. The representation theory of the symmetric groups. Lecture Notes in Math., vol. 682, Berlin, New York, Springer-Verlag, 1978.
Received:
14.03.2014
Accepted:
04.08.2014
Published:
10.09.2014
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