Action on flag varieties: 2-Dimensional case |
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Authors: | Dae San Kim Myung-Hwan Kim Jae Moon Kim |
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Institution: | (1) Department of Mathematics, Seoul Woman's University, 139-774 Seoul, Korea;(2) Department of Mathematics, Seoul National University, 151-742 Seoul, Korea;(3) Department of Mathematics, Inha University, 402-751 Inchon, Korea |
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Abstract: | LetA be a finite dimensional commutative semisimple algebra over a fieldk and letV be a finitely generatedA-module. We examine the action of the general linear group GL
A
(V) on the set of flags ofk-subspaces ofV. Also, let (V, B) be a finitely generated symplectic module overA. We also investigate the action of the symplectic group Sp
A
(V, B) on the set of flags ofB -isotropick-subspaces ofV, whereB = °B is thek-symplectic form induced by a nonzerok-linear map :A k. In both cases, the orbits are completely classified in terms of certain integer invariants provided that dim
k A=2.This work is partially supported by a KOSEF research grant. |
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