On closures of orbits and arithmetic of quaternions

Shahar Mozes

doi:10.1007/BF02773677

On closures of orbits and arithmetic of quaternions

Shahar Mozes^*

^*Corresponding author for this work

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

9 Scopus citations

Abstract

For G=PGL₂(ℚ_p )×PGL₂ ℚ we study the closures of orbits under the maximal split Cartan subgroup of G in homogeneous spaces Γ\G. We show that if a closure of an orbit contains a closed orbit then the orbit is either dense or closed. We show the relation of this to divisibility properties of integral quaternions and other lattices.

Original language	English
Pages (from-to)	195-209
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	86
Issue number	1-3
DOIs	https://doi.org/10.1007/BF02773677
State	Published - Oct 1994
Externally published	Yes

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abstract = "For G=PGL2(ℚ p )×PGL2 ℚ we study the closures of orbits under the maximal split Cartan subgroup of G in homogeneous spaces Γ\textbackslash{}G. We show that if a closure of an orbit contains a closed orbit then the orbit is either dense or closed. We show the relation of this to divisibility properties of integral quaternions and other lattices.",

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AB - For G=PGL2(ℚ p )×PGL2 ℚ we study the closures of orbits under the maximal split Cartan subgroup of G in homogeneous spaces Γ\G. We show that if a closure of an orbit contains a closed orbit then the orbit is either dense or closed. We show the relation of this to divisibility properties of integral quaternions and other lattices.

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On closures of orbits and arithmetic of quaternions

Abstract

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