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arXiv · 1903.05957

The Atiyah-Sutcliffe Determinant

Joseph Malkoun
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Abstract

We present a general formula for the Atiyah-Sutcliffe determinant function, which holds for any integer $n \geq 2$, as a global factor times a sum of terms, with each term similar to a higher degree cross-ratio. The formula is to our knowledge new. We also conjecture that the Atiyah-Sutcliffe determinant is a rational linear combination of products of factors of only two simple types, each of them manifestly $SO(3)$-invariant. This allows us to obtain a conjectural purely angular formula for the determinant for $n=4$, as an illustration of how our conjecture can be applied.

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Joseph Malkoun. 2019-03-14. The Atiyah-Sutcliffe Determinant. https://arxiv.org/abs/1903.05957

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