Maslov Index and a Central Extension of the Symplectic Group |
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| Authors: | R Parimala R Preeti and R Sridharan |
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| Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India;(2) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India;(3) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India |
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| 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 I
2(K) and that the induced natural homomorphism from K
2
Sp(K)I
2(K) is indeed the homomorphism given by the symplectic symbol {x, y} mapping to the Pfister form  1, -x  1, –y. |
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| Keywords: | Maslov index symplectic symbols Witt-group |
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