Odd symplectic flag manifolds

Details Odd symplectic flag manifolds Odd symplectic flag manifolds

2006-04-13

arxiv.org/abs/math/0604323v1

Mathematics

Algebraic Geometry

32 pages

Scientific paper

We define the odd symplectic grassmannians and flag manifolds, which are smooth projective varieties equipped with an action of the odd symplectic group and generalizing the usual symplectic grassmannians and flag manifolds. Contrary to the latter, which are the flag manifolds of the symplectic group, the varieties we introduce are not homogeneous. We argue nevertheless that in many respects the odd symplectic grassmannians and flag manifolds behave like homogeneous varieties; in support of this claim, we compute the automorphism group of the odd symplectic grassmannians, and we prove a Borel-Weil type theorem for the odd symplectic group.

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