Abstract
In this paper, we find some necessary and sufficient conditions on the dimension vector d{combining low line}=(d1,...,dk;n) so that the diagonal action of PGL(n) on ∏i=1kGr(di;n) has a dense orbit. Consequently, we obtain some algorithms for finding dense and sparse dimension vectors and classify dense dimension vectors with small length or size. We also classify dimension vectors where |di-dj|<3 for all i, j generalizing a theorem of Popov [11].
Original language | English |
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Pages (from-to) | 75-102 |
Number of pages | 28 |
Journal | Journal of Algebra |
Volume | 429 |
DOIs | |
State | Published - May 1 2015 |
Keywords
- Dense orbits
- Grassmannians
- PGL(n) actions