Polar Decomposition for P-adic Symmetric Spaces
نویسنده
چکیده
Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution σ of G. We prove a polar decomposition G = KAH for the symmetric space G/H over any local field k of characteristic not 2. Here K is a compact subset of G and A is a finite union of groups Ai which are the k-points of maximal (k, σ)-split tori, one for each H-conjugacy class. This decomposition is analogous to the well-known polar decomposition G = KAH for a real symmetric space G/H .
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