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	American 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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10.1007/BF02773677

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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\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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