An example of orthogonal triple flag variety of finite type

Details An example of orthogonal triple flag variety of finite type An example of orthogonal triple flag variety of finite type

2010-11-30

arxiv.org/abs/1011.6468v2

Mathematics

Representation Theory

38pages, modified references in p.1 and p.5

Scientific paper

Let G be the split special orthogonal group of degree 2n+1 over a field F of char F \ne 2. Then we describe G-orbits on the triple flag varieties G/P\times G/P\times G/P and G/P\times G/P\times G/B with respect to the diagonal action of G where P is a maximal parabolic subgroup of G of the shape (n,1,n) and B is a Borel subgroup. As by-products, we also describe GL_n-orbits on G/B, Q_{2n}-orbits on the full flag variety of GL_{2n} where Q_{2n} is the fixed-point subgroup in Sp_{2n} of a nonzero vector in F^{2n} and 1\times Sp_{2n}-orbits on the full flag variety of GL_{2n+1}. In the same way, we can also solve the same problem for SO_{2n} where the maximal parabolic subgroup P is of the shape (n,n).

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