  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 associated with the
representation and an algebraic basis which consists of its minimal
idempotents. The transition matrix involves combinatorial invariants of
lattices of submodules of finite O-modules. The idempotents are p-adic analogs
of the multivariable Jacobi polynomials.
