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We classify pairs of hyperbolic elements in $Sp(2,1)$ up to conjugation.\n  A hyperbolic element of $Sp(2,1)$ is called `loxodromic' if it has no real eigenvalue. We show that the set of $Sp(2,1)$ conjugation orbits of irreducible loxodromic pairs is a $(\\mathbb C {\\mathbb P}^1)^4$-bundle over a topological space that is locally a semi-analytic subspace of ${\\mathbb R}^{13}$. 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Kalane","submitted_at":"2017-08-21T01:16:25Z","abstract_excerpt":"Let $Sp(2,1)$ be the isometry group of the quaternionic hyperbolic plane ${{\\bf H}_{\\mathbb H}}^2$. An element $g$ in $Sp(2,1)$ is `hyperbolic' if it fixes exactly two points on the boundary of ${{\\bf H}_{\\mathbb H}}^2$. We classify pairs of hyperbolic elements in $Sp(2,1)$ up to conjugation.\n  A hyperbolic element of $Sp(2,1)$ is called `loxodromic' if it has no real eigenvalue. We show that the set of $Sp(2,1)$ conjugation orbits of irreducible loxodromic pairs is a $(\\mathbb C {\\mathbb P}^1)^4$-bundle over a topological space that is locally a semi-analytic subspace of ${\\mathbb R}^{13}$. 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