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Zap. Nauchn. Sem. POMI, 2006, Volume 338, Pages 69–97 (Mi znsl166)  

This article is cited in 8 scientific papers (total in 8 papers)

Polyvector representations of $\operatorname{GL}_n$

N. A. Vavilov, E. Ya. Perelman

Saint-Petersburg State University

Abstract: In the present paper we characterise $\bigwedge^n(\operatorname{GL}(n,R))$ over any commutative ring $R$ as the connected component of the stabiliser of Plücker ideal. This folk theorem is classically known for algebraically closed fields and should be also well-known in general. However, we are not aware of any obvious reference, so we produce a detailed proof which follows a general scheme developed by W. C. Waterhouse. The present paper is a technical preliminary for a subsequent paper, where we construct decomposition of transvections in polyvector representations of $\operatorname{GL}_n$.

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English version:
Journal of Mathematical Sciences (New York), 2007, 145:1, 4737–4750

Bibliographic databases:

UDC: 512.5
Received: 23.10.2006

Citation: N. A. Vavilov, E. Ya. Perelman, “Polyvector representations of $\operatorname{GL}_n$”, Problems in the theory of representations of algebras and groups. Part 14, Zap. Nauchn. Sem. POMI, 338, POMI, St. Petersburg, 2006, 69–97; J. Math. Sci. (N. Y.), 145:1 (2007), 4737–4750

Citation in format AMSBIB
\by N.~A.~Vavilov, E.~Ya.~Perelman
\paper Polyvector representations of $\operatorname{GL}_n$
\inbook Problems in the theory of representations of algebras and groups. Part~14
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 338
\pages 69--97
\publ POMI
\publaddr St.~Petersburg
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 145
\issue 1
\pages 4737--4750

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    This publication is cited in the following articles:
    1. N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm{E}_6$”, Algebra i analiz, 19:5 (2007), 37–64  mathnet  mathscinet  zmath; N. A. Vavilov, A. Yu. Luzgarev, “The normalizer of Chevalley groups of type $\mathrm{E}_6$”, St. Petersburg Math. J., 19:5 (2008), 699–718  crossref  isi
    2. Vavilov N., “An $A_3$-proof of structure theorems for Chevalley groups of types $E_6$ and $E_7$”, Internat. J. Algebra Comput., 17:5-6 (2007), 1283–1298  crossref  mathscinet  zmath  isi  elib
    3. N. A. Vavilov, “Numerologiya kvadratnykh uravnenii”, Algebra i analiz, 20:5 (2008), 9–40  mathnet  mathscinet  zmath; N. A. Vavilov, “Numerology of square equations”, St. Petersburg Math. J., 20:5 (2009), 687–707  crossref  isi
    4. A. S. Ananievskiy, N. A. Vavilov, S. S. Sinchuk, “Overgroups of $E(m,R)\otimes E(n,R)$”, J. Math. Sci. (N. Y.), 161:4 (2009), 461–473  mathnet  crossref  elib
    5. N. A. Vavilov, V. G. Kazakevich, “More variations on decomposition of transvections”, J. Math. Sci. (N. Y.), 171:3 (2010), 322–330  mathnet  crossref
    6. A. S. Ananevskii, N. A. Vavilov, S. S. Sinchuk, “O nadgruppakh $E(m,R)\otimes E(n,R)$. I. Urovni i normalizatory”, Algebra i analiz, 23:5 (2011), 55–98  mathnet  mathscinet  elib; A. S. Ananyevskiy, N. A. Vavilov, S. S. Sinchuk, “Overgroups of $E(m,R)\otimes E(n,R)$. I”, St. Petersburg Math. J., 23:5 (2012), 819–849  crossref  isi  elib
    7. N. A. Vavilov, “Decomposition of unipotents for $\mathrm E_6$ and $\mathrm E_7$: 25 years after”, Voprosy teorii predstavlenii algebr i grupp. 27, Zap. nauchn. sem. POMI, 430, POMI, SPb., 2014, 32–52  mathnet  mathscinet; J. Math. Sci. (N. Y.), 219:3 (2016), 355–369  crossref
    8. N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm E_7$”, Algebra i analiz, 27:6 (2015), 57–88  mathnet  mathscinet  elib; N. A. Vavilov, A. Yu. Luzgarev, “Normaliser of the Chevalley group of type $\mathrm E_7$”, St. Petersburg Math. J., 27:6 (2016), 899–921  crossref  isi
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