On the Hilbert series of the Grassmannian

Lukas Braun

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arXiv · 1712.05747

On the Hilbert series of the Grassmannian

Lukas Braun

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Abstract

We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods and show that its h-polynomial coincides with the k-Narayana polynomial. We give a simplified formula for the h-polynomial of Schubert varieties. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the k-Narayana numbers, i.e. the h-polynomial of the Grassmannian.

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Lukas Braun. 2017-12-15. On the Hilbert series of the Grassmannian. https://arxiv.org/abs/1712.05747

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