Topics in Representation Theory: Other Topics
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چکیده
• Topology of G/T : Flag manifolds G/T have cohomology only in even degrees, with Euler characteristic the degree of the Weyl group. The Euler characteristic can be calculated by a Lefschetz fixed point argument (see Adams [1], pgs. 90-92 for this). Identifying the flag manifold with a co-adjoint orbit, there is a Morse theory calulation of the cohomology that goes back to Bott, for an outline of the story, see [2]. This can also be thought of as a simple example of a torus action on a Kähler manifold, exhibiting the phenomenon of the moment map giving a perfect Morse function.
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