THE MODULI SPACE OF POINTS IN THE BOUNDARY OF QUATERNIONIC HYPERBOLIC SPACE

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Let F_1(n,m) be the PSp(n, 1)-configuration space of ordered m-tuple of pairwise distinct points in the boundary of quaternionic hyperbolic n-space ∂𝗛^n_H , i.e., the m-tuple of pairwise distinct points in ∂𝗛^n_H up to the diagonal action of PSp(n, 1). In terms of Cartan’s angular invariant and cross-ratio invariants, the moduli space of F1(n,m) is described by using Moore’s determinant. We show that the moduli space of F_1(n,m) is a real 2m^2 − 6m + 5 − Σ^＜m−n−1＞ _＜i=1＞ ( ^＜m−2＞_＜n−1+i＞) dimensional subset of a algebraic variety with the same real dimension when m > n+1.

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  • Osaka Journal of Mathematics

    Osaka Journal of Mathematics 57 (4), 827-846, 2020-10

    Osaka University and Osaka City University, Departments of Mathematics

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