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Article Dans Une Revue Communications in Mathematics Année : 2019

Hilbert series of the Grassmannian and k-Narayana numbers

Lukas Braun
  • Fonction : Auteur correspondant

Résumé

We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the q-Hilbert series is a Vandermonde-like determinant. We show that the h-polynomial of the Grassmannian coincides with the k-Narayana polynomial. A simplified formula for the h-polynomial of Schubert varieties is given. 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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hal-03664962 , version 1 (11-05-2022)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Lukas Braun. Hilbert series of the Grassmannian and k-Narayana numbers. Communications in Mathematics, 2019, Volume 27 (2019), Issue 1 (1), pp.27 - 41. ⟨10.2478/cm-2019-0003⟩. ⟨hal-03664962⟩
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