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We study a family of complex representations of the group GL n (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 GL n (F) to its maximal compact subgroup GL n (o). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra(More)
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 n. We introduce some invariants of the double cosets. If k is the length of the ring, we(More)
We define a new notion of cuspidality for representations of GL n over a finite quotient o k of the ring of integers o of a non-Archimedean local field F using geometric and infinitesimal induction functors, which involve automorphism groups G λ 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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