In this paper we prove local-global principles for embedding of fields withinvolution into central simple algebras with involution over a global field.These should be of interest in study of classical groups over global fields. Wededuce from our results that in a group of type D_n, n>4 even, two weaklycommensurable Zariski-dense S-arithmetic subgroups are actually commensurable.A consequence of this result is that given an absolutely simple algebraicK-group G of type D_n, n>4 even, K a number field, any K-form G' of G havingthe same set of isomorphism classes of maximal K-tori as G, is necessarilyK-isomorphic to G. These results lead to results about isolength andisospectral compact hyperbolic spaces of dimension 2n-1 with n even.
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