1. bookVolume 27 (2019): Issue 1 (June 2019)
Journal Details
License
Format
Journal
eISSN
2336-1298
First Published
16 Jun 2010
Publication timeframe
2 times per year
Languages
English
access type Open Access

Hilbert series of the Grassmannian and k-Narayana numbers

Published Online: 04 Jul 2019
Volume & Issue: Volume 27 (2019) - Issue 1 (June 2019)
Page range: 27 - 41
Received: 04 Jun 2018
Accepted: 18 Dec 2018
Journal Details
License
Format
Journal
eISSN
2336-1298
First Published
16 Jun 2010
Publication timeframe
2 times per year
Languages
English
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.

Keywords

MSC 2010

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