Index functions for symplectic paths

In this chapter, we introduce an index function theory for paths in the symplectic groups started from the identity, i.e., elements in P_τ(2n) with τ > 0 defined by (2.0.1): . For τ> 0 and ω∈U, we further define the set of ω-non-degenerate paths by and the set of ω-degenerate paths by .