# Symplectic Geometry by Carl Ludwig Siegel (Auth.)

By Carl Ludwig Siegel (Auth.)

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Extra info for Symplectic Geometry

Example text

On the other hand, let us consider the definition of a discrete group. A group of matrices 99Î with real (or complex) elements is called discrete, if every infinite sequence of different 3JÎ diverges. I t is obvious that a discontinuous group of symplectic matrices is discrete. Let us now prove the con- 25 SYMPLECTIC GEOMETKY. for 3 = i&> an d consequently On the other hand, (56) άω — 2™ \ g) I»"1 Π {dxkidykl) = 2"1 Π (dxkidYkl) with (Yki) — g)"1. )-S we obtain, by (51), (55) and (56), x = Cn(—^ynin+1)/2 where the positive rational number is defined in (53), (»54) and (57) 2n*[(n2 + f dV9 F n)/2]l dv — U (dxjcidYbi) k