Maximal subgroups of the classical groups associated with non-isotropic subspaces of a vector space

AbstractThe maximal subgroups of the finite classical groups are divided by a theorem of Aschbacher into nine classes. In this paper, the authors show how to construct those maximal subgroups of the finite classical groups of linear, symplectic or unitary type that lie in the first eight of these classes. The ninth class consists roughly of absolutely irreducible groups that are almost simple modulo scalars, other than classical groups over the same field in their natural representation. All of these constructions can be carried out in low-degree polynomial time.

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Equivariant Giambelli formula for the symplectic Grassmannians — Pfaffian Sum Formula

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.2522 ◽

2015 ◽

Vol DMTCS Proceedings, 27th... (Proceedings) ◽

Author(s):

Takeshi Ikeda ◽

Tomoo Matsumura

Keyword(s):

Vector Space ◽

Closed Formula ◽

International Audience ◽

Sum Formula ◽

Isotropic Subspaces ◽

Espace Vectoriel ◽

Symplectic Vector Space ◽

Symplectic Grassmannians ◽

Schubert Class

International audience We prove an explicit closed formula, written as a sum of Pfaffians, which describes each equivariant Schubert class for the Grassmannian of isotropic subspaces in a symplectic vector space On démontre une formule close explicite, écrite comme une somme de Pfaffiens, qui décrit toute classe de Schubert équivariante pour la Grassmannienne des sous-espaces isotropes dans un espace vectoriel symplectique.

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On Invariants of Some Maximal Subgroups of Finite Classical Groups

Algebra Colloquium ◽

10.1142/s1005386712000107 ◽

2012 ◽

Vol 19 (01) ◽

pp. 149-158

Author(s):

Jizhu Nan ◽

Yufang Qin

Keyword(s):

Polynomial Rings ◽

Maximal Subgroups ◽

Linear Groups ◽

Classical Groups ◽

Invariant Rings ◽

Finite Classical Groups ◽

Finite Linear

The maximal subgroups of the finite classical groups are divided into nine classes by Aschbacher's theorem. In this paper, we give explicit transcendental bases of the invariant subfields of those maximal subgroups of classical groups of linear, symplectic and unitary cases that lie in the first two of these classes. Also, we show that the invariant rings of the maximal subgroups of the finite linear groups that lie in the first class are polynomial rings.

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