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Aug 25, 2017 at 12:59 comment added Allen Knutson It is not. The relation between the two was studied deeply in Kostant's "Lie algebra cohomology and generalized Schubert cells", where he conjugates $g$ by a one-parameter subgroup, and studies the limit, at which the Schubert classes are indeed harmonic in a suitable sense.
Jul 28, 2017 at 19:59 history edited Han Jin Ma
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Jul 27, 2017 at 16:26 history asked Han Jin Ma CC BY-SA 3.0