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Mar 18 at 18:35 comment added Vladimir Dotsenko @AlexanderBraverman In arxiv.org/abs/2112.12436 Nicolas Perrin and Maxim Smirnov state, in Lemma 4.6, part 3, a simple formula for the degree of the Schubert class corresponding to the root $\alpha$, leading to a simple formula for the Poincaré polynomial. (They refer to the article cited in my answer where this formula is not proved, but I think it should be easy to prove it directly - I just do not have time for this at the moment.)
Mar 18 at 17:41 comment added Alexander Braverman Ok, thanks, the Euler characteristic formula is indeed obvious, but I wonder if there is a simple formula for the Poincare polynomial.
Mar 18 at 15:51 history edited Vladimir Dotsenko CC BY-SA 4.0
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Mar 18 at 5:06 history answered Vladimir Dotsenko CC BY-SA 4.0