On geometry of curves of flags of constant type

• Autorzy: Boris Doubrov , Igor Zelenko
• Języki publikacji: EN

Abstrakty

EN

We develop an algebraic version of Cartan’s method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of a subgroup G of GL(W). Under some natural assumptions on the subgroup G and on the flags, one can pass from the filtered objects to the corresponding graded objects and describe the construction of canonical bundles of moving frames for these curves in the language of pure linear algebra. The scope of applicability of the theory includes geometry of natural classes of curves of flags with respect to reductive linear groups or their parabolic subgroups. As simplest examples, this includes the projective and affine geometry of curves. The case of classical groups is considered in more detail.

Słowa kluczowe

EN

Curves and submanifolds in flag varieties; Equivalence problem; Bundles of moving frames; Graded Lie algebras; Tanaka prolongation; sl2-representations

Kategorie tematyczne

• 17B70: Graded Lie (super)algebras
• 53B25: Local submanifolds
• 53A55: Differential invariants (local theory), geometric objects
• 53B15: Other connections

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 5
• Strony: 1836-1871

Daty

wydano

2012-10-01

online

2012-07-24

Twórcy

autor

Boris Doubrov

• Belarussian State University

autor

Igor Zelenko

• Texas A&M University

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0078-7