Hilbert series of the Grassmannian and k-Narayana numbers - Archive ouverte HAL Access content directly
Journal Articles Communications in Mathematics Year : 2019

Hilbert series of the Grassmannian and k-Narayana numbers

Lukas Braun
  • Function : Correspondent author

Abstract

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.
Fichier principal
Vignette du fichier
10-2478-cm-2019-0003.pdf (342.26 Ko) Télécharger le fichier
Origin : Explicit agreement for this submission

Dates and versions

hal-03664962 , version 1 (11-05-2022)

Licence

Attribution - NonCommercial - NoDerivatives

Identifiers

Cite

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⟩

Collections

INSMI
11 View
187 Download

Altmetric

Share

Gmail Facebook X LinkedIn More