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Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine(More)
We study a family of complex representations of the group GLn(o), where o is the ring of integers of a non-archimedean local field F . These representations occur in the restriction of the Grassmann representation of GLn(F ) to its maximal compact subgroup GLn(o). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra(More)
We define a new notion of cuspidality for representations of GLn over a finite quotient ok of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups Gλ of torsion o-modules. When n is a prime, we show that this notion of cuspidality is equivalent to strong(More)
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