Abstract
(iii) semi-involutions (Q IQ VQ QJ where Q is a diagonal matrix of zeros and ones. Then [1] Sp(2n) is generated by the set of rotations, translations, and semi-involutions. Let Ei, be the n by n matrix, all zero except for a one in the ijth entry. Let Rij(x) be the rotation, as above, with A =I+xEji, for i $j; T,(x) the translation with S=xE,i; and Ti(x) the translation with S=xE,j+xEji. Then the T's commute and (2) (T,(x))?*= T,(?kx), (Tqj(x))?k = Tij(?kx), k any integer. If we let (U, V) be the commutator, UVUV-1, then
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