What question did this study set out to answer?

To investigate strongly doubly reversible pairs in the quaternionic unitary group and related spaces.

December 22, 2025Open Access

Strongly Doubly Reversible Pairs in Quaternionic Unitary Group of Signature (n, 1)

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The study reveals pairs in the isometry group of quaternionic hyperbolic space, indicating Haar measure zero exists for such pairs.

To investigate strongly doubly reversible pairs in the quaternionic unitary group and related spaces.
Examined pairs in $ ext{PSp}(n,1)$ and $ ext{PSp}(n)$ for Haar measure properties.
Showed that in $ ext{PSp}(1)$ all pairs are strongly doubly reversible.
Derived conditions for hyperbolic elements in $ ext{PSp}(1,1)$.
Identified that the set of strongly doubly reversible pairs has Haar measure zero in $ ext{PSp}(n,1) \times ext{PSp}(n,1)$.
Confirmed that every pair of elements in $ ext{SO}(4)$ is strongly doubly reversible.

Gongopadhyay et al. (2025) studied this question.

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