| Title:
|
Hilbert series of the Grassmannian and $k$-Narayana numbers (English) |
| Author:
|
Braun, Lukas |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
27-41 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
Hilbert series of the Grassmannian |
| Keyword:
|
Narayana numbers |
| Keyword:
|
Euler's hypergeometric transform |
| MSC:
|
13D40 |
| MSC:
|
14M15 |
| MSC:
|
33C90 |
| idZBL:
|
Zbl 1467.13024 |
| idMR:
|
MR3977475 |
| . |
| Date available:
|
2019-06-28T14:47:22Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147766 |
| . |
| Reference:
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