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Acta Mathematica Vietnamica

NOTES ON YOSHIDA’S COORDINATES ON HITCHIN’S PRYM COVER

SØREN KOLD HANSEN, DANIEL MOSKOVICH

Abstract

As the first stage of his proposed geometric quantization of the SU(2) WZW model, T. Yoshida introduced coordinates on a Prym variety which covers the moduli space of semi-stable rank 2 vector bundles with trivial determinant over a Riemann surface [13]. We explain Yoshida’s coordinates, and reprove their key properties using elementary combinatorial arguments.