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Polyvector representations of GLn

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Abstract

In the present paper, we characterize ⋀n(GL(n, R)) over any commutative ring R as the connected component of the stabilizer of the Plücker ideal. This folk theorem is classically known for algebraically closed fields and should also be 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 to a subsequent paper, where we construct the decomposition of transvections in polyvector representations of GL n. Bibliography: 50 titles.

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  1. St. Petersburg State University, St. Petersburg, Russia

    N. A. Vavilov & E. Ya. Perelman

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  1. N. A. Vavilov
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  2. E. Ya. Perelman
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 338, 2006, pp. 69–97.

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Vavilov, N.A., Perelman, E.Y. Polyvector representations of GLn . J Math Sci 145, 4737–4750 (2007). https://doi.org/10.1007/s10958-007-0305-0

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