Comparison of the Bruhat and the Iwahori decompositions of a \(p\)-adic Chevalley group (Q1333214)

Let \(G\) be a \(p\)-adic Chevalley group. The decomposition of \(G\) into double cosets under a Borel subgroup, the Bruhat decomposition, is indexed by the small Weyl group of \(G\). An Iwahori subgroup, i.e. the inverse image of a Borel subgroup of the finite quotient, gives a double coset decomposition indexed by the big Weyl group. In the paper the author introduces an ``integer structure'' on the Bruhat cells to get a refined decomposition, again indexed by the big Weyl group. A comparison theorem then gives a criterion in terms of the Weyl group to decide when two cells of the two types have a nonvoid intersection.