Decomposition of transvections: An algebro-geometric approach

Petrov, Viktor

doi:10.1090/spmj/1440

Cited by 5 publications

(2 citation statements)

References 9 publications

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“…Almost at once Nikolai Vavilov generalized this result to other split classical groups [16], and in 1990 Nikolai Vavilov, Alexei Stepanov, and Eugene Plotkin developed the method for exceptional groups [23]. Since the 1990s the decomposition of unipotents was the focus of a number of authors, see [5,11,12,17,20] for further references.…”

Section: Introductionmentioning

confidence: 99%

The reverse decomposition of unipotents for bivectors

Lubkov¹

2021

Preprint

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For the second fundamental representation of the general linear group over a commutative ring R we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary matrix and its inverse. Towards the solution we get stabilization theorems for any column of a matrix from GL ( n 2 ) (R) or from the exterior square of GLn(R), n 3.

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Section: Introductionmentioning

confidence: 99%

The reverse decomposition of unipotents for bivectors

Lubkov¹

2021

Preprint

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“…The next generation of the SCT proofs works for Chevalley groups. L. Vaserstein [15] and E. Abe [1] used localization methods whereas N. Vavilov, E. Plotkin and A. Stepanov [22] introduced the decomposition of unipotents, which in more detail was described in [13] and further developed in [18,19,21,20,16,17] by Vavilov and his students and in [8] by V. Petrov. For generalized hyperbolic unitary groups the SCT was announced by A. Bak and N. Vavilov in [3], but the proof has never been published.…”

Section: Introductionmentioning

confidence: 99%

Sandwich classification for O _2n+1(R) and U _2n+1(R,Δ) revisited

Preusser

2018

Journal of Group Theory

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In a recent paper, the author proved that if n ě 3 is a natural number, R a commutative ring and σ P GLnpRq, then t kl pσij q where i ‰ j and k ‰ l can be expressed as a product of 8 matrices of the form ǫ σ˘1 where ǫ P EnpRq. In this article we prove similar results for the odd-dimensional orthogonal groups O2n`1pRq and the odd-dimensional unitary groups U2n`1pR, ∆q under the assumption that R is commutative and n ě 3. This yields new, short proofs of the Sandwich Classification Theorems for the groups O2n`1pRq and U2n`1pR, ∆q.

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