On some geometric representations of GL(n,O)

Details On some geometric representations of GL(n,O) On some geometric representations of GL(n,O)

2004-04-22

arxiv.org/abs/math/0404408v2

Mathematics

Representation Theory

19 pages, revised version

Scientific paper

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.

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