Geodesic
Reverse decomposition of unipotents in polyvector representations
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 120-138 Cet article a éte moissonné depuis la source Math-Net.Ru

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The present paper continues the series of papers devoted to the method of decomposition of unipotents and its numerous variations. For exterior square of the general linear group, which is a key particular case of exterior powers, the question of the reverse decomposition of unipotents was considered by the author (2021). A generalization of the obtained results to an arbitrary exterior power is discussed. 
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     author = {R. Lubkov},
     title = {Reverse decomposition of unipotents in polyvector representations},
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     pages = {120--138},
     year = {2022},
     volume = {513},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a8/}
}
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R. Lubkov. Reverse decomposition of unipotents in polyvector representations. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 38, Tome 513 (2022), pp. 120-138. http://geodesic.mathdoc.fr/item/ZNSL_2022_513_a8/

[1] N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{EO (2l,R)}$”, Zap. nauchn. semin. POMI, 272, 2000, 68–85 | MR

[2] N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{Ep (2l,R)}$”, Algebra i Analiz, 15:4 (2003), 72–114 | MR

[3] N. A. Vavilov, E. Ya. Perelman, “Polivektornye predstavleniya $\mathrm{GL}_n$”, Zap. nauchn. semin. POMI, 338, 2006, 69–97

[4] N. A. Vavilov, A. Yu. Luzgarev, “Normalizator gruppy Shevalle tipa $\mathrm{E}_6$”, Algebra i Analiz, 19:5 (2007), 37–64

[5] N. A. Vavilov, V. A. Petrov, “O nadgruppakh $\mathrm{EO}(n,R)$”, Algebra i Analiz, 19:2 (2007), 10–51 | MR

[6] N. A. Vavilov, V. G. Kazakevich, “Esche neskolko variatsii na temu razlozheniya transvektsii”, Zap. nauchn. semin. POMI, 375, 2010, 32–47

[7] R. A. Lubkov, I. I. Nekrasov, “Yavnye uravneniya na vneshnii kvadrat polnoi lineinoi gruppy”, Zap. nauchn. semin. POMI, 470, 2018, 120–137

[8] V. A. Petrov, “Razlozhenie transvektsii: algebro-geometricheskii podkhod”, Algebra i Analiz, 28:1 (2016), 150–157 | MR

[9] A. V. Stepanov, “Novyi vzglyad na razlozhenie unipotentov i normalnoe stroenie grupp Shevalle”, Algebra i Analiz, 28:3 (2016), 161–173

[10] R. Hazrat, N. Vavilov, Z. Zhang, “Relative commutator calculus in Chevalley groups”, J. Algebra, 385 (2013), 262–293 | DOI | MR

[11] R. Lubkov, “The reverse decomposition of unipotents for bivectors”, Comm. Algebra, 49:10 (2021), 4546–4556 | DOI | MR

[12] R. Lubkov, I. Nekrasov, “Overgroups of exterior powers of an elementary group. I. Levels and normalizers”, Linear and multilinear algebra, 2021 (to appear) , 20 pp.; arXiv: 1801.07918

[13] R. Lubkov, A. Stepanov, “Subgroups of Chevalley groups over rings”, Zap. nauchn. semin. POMI, 484, 2019, 121–137 | MR

[14] E. B. Plotkin, A. A. Semenov, N. A. Vavilov, “Visual basic representations: an atlas”, Internat. J. Algebra Comput., 8:1 (1998), 61–95 | DOI | MR

[15] R. Preusser, “Structure of hyperbolic unitary groups II: Classification of E-normal subgroups”, Algebra Colloq., 24:2 (2017), 195–232 | DOI | MR

[16] R. Preusser, “Sandwich classification for $O_{2n+1}(R)$ and $U_{2n+1}(R,\Delta)$ revisited”, J. Group Theory, 21:4 (2018), 539–571 | DOI | MR

[17] R. Preusser, “Sandwich classification for ${\rm GL}_n(R)$, ${\rm O}_{2n}(R)$ and ${\rm U}_{2n}(R,\Lambda)$ revisited”, J. Group Theory, 21:1 (2018), 21–44 | DOI | MR

[18] A. V. Stepanov, N. A. Vavilov, “Decomposition of transvections: Theme with variations”, K-Theory, 19:2 (2000), 109–153 | DOI | MR

[19] N. A. Vavilov, “Decomposition of unipotents for $E_6$ and $E_7$: 25 years after”, Zap. nauchn. semin. POMI, 430, 2014, 32–52 | MR