Hilbert series of the Grassmannian and k-Narayana numbers
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2019
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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.
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lukas2019hilbertcommunications
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| Authors | Lukas, Braun; |
| Journal | communications in mathematics |
| Year | 2019 |
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