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Canonical Forms for Conjugacy Classes of Prime Order Symplectic Matrices in Sp(2g, Z)

We solve the following problem: Let M be a 2g × 2g symplectic matrix of prime order with integer entries. Find a unique normal form for M , that is, a symplectic matrix whose entries are determined by its conjugacy invariants. This is equivalent to finding a unique normal form for the matrix representation of the conjugacy class of a prime order element of the mapping class group.