## Lukas Braun - Hilbert series of the Grassmannian and k-Narayana numbers

cm:9485 - Communications in Mathematics, July 4, 2019, Volume 27 (2019), Issue 1 - https://doi.org/10.2478/cm-2019-0003
Hilbert series of the Grassmannian and k-Narayana numbers

Authors: Lukas Braun

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.

Volume: Volume 27 (2019), Issue 1
Published on: July 4, 2019
Imported on: May 11, 2022
Keywords: [MATH]Mathematics [math]