Polar decomposition for p-adic symmetric spaces

Details Polar decomposition for p-adic symmetric spaces Polar decomposition for p-adic symmetric spaces

2006-12-12

arxiv.org/abs/math/0612305v1

Mathematics

Group Theory

16 pages

Scientific paper

Let G be the group of k-points of a connected reductive k-group and H a symmetric subgroup associated to an involution s 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 the groups of k-points of maximal (k,s)-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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