Geodesic
Overgroups of exterior powers of an elementary group. Normalizers
Documenta mathematica, Tome 29 (2024) no. 5, pp. 1243-1268 Cet article a éte moissonné depuis la source EMS Press

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We establish two characterizations of an algebraic group scheme ⋀mGLn​ over Z. Geometrically, the scheme ⋀mGLn​ is a stabilizer of an explicitly given invariant form or, generally, an invariant ideal of forms. Algebraically, ⋀mGLn​ is isomorphic (as a scheme over Z) to a normalizer of the elementary subgroup functor ⋀mEn​ and a normalizer of the subscheme ⋀mSLn​. Our immediate goal is to apply both descriptions in the “sandwich classification” of overgroups of the elementary subgroup. Additionally, the results can be seen as a solution of the linear preserver problem for algebraic group schemes over Z, providing a more functorial description that goes beyond geometry of the classical case over fields.
DOI : 10.4171/dm/956
Classification : 20G35, 14L15, 15A69
Mots-clés : general linear group, exterior power, elementary subgroup, invariant forms, Plucker polynomials, linear preserver problems 
@article{10_4171_dm_956,
     author = {Roman Lubkov and Ilia Nekrasov},
     title = {Overgroups of exterior powers of an elementary group. {Normalizers}},
     journal = {Documenta mathematica},
     pages = {1243--1268},
     year = {2024},
     volume = {29},
     number = {5},
     doi = {10.4171/dm/956},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/956/}
}
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Roman Lubkov; Ilia Nekrasov. Overgroups of exterior powers of an elementary group. Normalizers. Documenta mathematica, Tome 29 (2024) no. 5, pp. 1243-1268. doi: 10.4171/dm/956

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