Dense PGL-orbits in products of Grassmannians

Izzet Coskun; Majid Hadian; Dmitry Zakharov

doi:10.1016/j.jalgebra.2015.01.019

Dense PGL-orbits in products of Grassmannians

Izzet Coskun, Majid Hadian, Dmitry Zakharov

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 |d_i-d_j|<3 for all i, j generalizing a theorem of Popov [11].

Original language	English
Pages (from-to)	75-102
Number of pages	28
Journal	Journal of Algebra
Volume	429
DOIs	https://doi.org/10.1016/j.jalgebra.2015.01.019
State	Published - May 1 2015

Keywords

Dense orbits
Grassmannians
PGL(n) actions

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10.1016/j.jalgebra.2015.01.019

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title = "Dense PGL-orbits in products of Grassmannians",

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].",

keywords = "Dense orbits, Grassmannians, PGL(n) actions",

author = "Izzet Coskun and Majid Hadian and Dmitry Zakharov",

note = "Funding Information: During the preparation of this article the first author was partially supported by the National Science Foundation CAREER grant DMS-0950951535 , and an Alfred P. Sloan Foundation Fellowship. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

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AU - Hadian, Majid

AU - Zakharov, Dmitry

N1 - Funding Information: During the preparation of this article the first author was partially supported by the National Science Foundation CAREER grant DMS-0950951535 , and an Alfred P. Sloan Foundation Fellowship. Publisher Copyright: © 2015 Elsevier Inc.

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N2 - 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].

AB - 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].

KW - Dense orbits

KW - Grassmannians

KW - PGL(n) actions

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M3 - Article

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VL - 429

SP - 75

EP - 102

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

Dense PGL-orbits in products of Grassmannians

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