Cite this article as:
Shulezhko O. V. New Properties of Almost Nilpotent Variety of Exponent 2 . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 3, pp. 316-320. DOI: https://doi.org/10.18500/1816-9791-2014-14-3-316-320
Language:
Russian
Heading:
UDC:
512.5
New Properties of Almost Nilpotent Variety of Exponent 2
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
1. Mishchenko S., Valenti A. An almost nilpotent variety of exponent 2. Israel J. of Math., 2014, vol. 199, iss. 1, pp. 241–257.
2. Giambruno A., Zaicev M. Polynomial Identities and Asymptotic Methods. Math. Surv. and Monographs, vol. 122, Providence, RI, Amer. Math. Soc., 2005, 352 p.
3. 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.
4. James G. D. The representation theory of the symmetric groups. Lecture Notes in Math., vol. 682, Berlin, New York, Springer-Verlag, 1978.
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