Maslov index and a central extension of the symplectic group

Abstract

In this paper we show that over any field K of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to I²(K) and that the induced natural homomorphism from K₂Sp(K)→I²(K) is indeed the homomorphism given by the symplectic symbol {x, y} mapping to the Pfister form (1,-x)⊗(1,–y).