Polynomial identities related to Special Schubert varieties

Francesca Cioffi; Davide Franco; Carmine Sessa

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arXiv · 2011.09806

Polynomial identities related to Special Schubert varieties

Francesca Cioffi·Davide Franco·Carmine Sessa

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Abstract

Let $\mathcal S$ be a single condition Schubert variety with an arbitrary number of strata. Recently, an explicit description of the summands involved in the decomposition theorem applied to such a variety has been obtained in a paper of the second author. Starting from this result, we provide an explicit description of the Poincar\'{e} polynomials of the intersection cohomology of $\mathcal S$ by means of the Poincar\'{e} polynomials of its strata, obtaining interesting polynomial identities relating Poincar\'{e} polynomials of several Grassmannians, both by a local and by a global point of view. We also present a symbolic study of a particular case of these identities.

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Francesca Cioffi, Davide Franco, Carmine Sessa. 2020-11-19. Polynomial identities related to Special Schubert varieties. https://arxiv.org/abs/2011.09806

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