Hilbert series of the Grassmannian and k-Narayana numbers-Reference-Cited by-同舟云学术

Hilbert series of the Grassmannian and k-Narayana numbers

Published:2019-06-01 Issue:1 Volume:27 Page:27-41
ISSN:2336-1298
Container-title:Communications in Mathematics
language:en
Short-container-title:

Author:

Braun Lukas¹

Affiliation:

1. Mathematisches Institut , Universität Tübingen , Auf der Morgenstelle 10, 72076 , Tübingen , Germany

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.sciendo.com/pdf/10.2478/cm-2019-0003

Reference22 articles.

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5. [5] B.H. Gross, N.R. Wallach: On the Hilbert polynomials and Hilbert series of homogeneous projective varieties. Arithmetic geometry and automorphic forms 19 (2011) 253–263.

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