9,571 research outputs found
Geometric representations of GL(n,R), cellular Hecke algebras and the embedding problem
We study geometric representations of GL(n,R) for a ring R. The structure of
the associated Hecke algebras is analyzed and shown to be cellular.
Multiplicities of the irreducible constituents of these representations are
linked to the embedding problem of pairs of R-modules x < y.Comment: 18 pages, final version, to appear in JPA
From p-adic to real Grassmannians via the quantum
Let F be a local field. The action of GL(n,F) on the Grassmann variety
Gr(m,n,F) induces a continuous representation of the maximal compact subgroup
of GL(n,F) on the space of L^2-functions on Gr(m,n,F). The irreducible
constituents of this representation are parameterized by the same underlying
set both for Archimedean and non-Archimedean fields.
This paper connects the Archimedean and non-Archimedean theories using the
quantum Grassmannian. In particular, idempotents in the Hecke algebra
associated to this representation are the image of the quantum zonal spherical
functions after taking appropriate limits. Consequently, a correspondence is
established between some irreducible representations with Archimedean and
non-Archimedean origin.Comment: 24 pages, final version, to appear in Advances in Mathematic
Representations of automorphism groups of finite O-modules of rank two
Let O be a complete discrete valuation domain with finite residue field. In
this paper we describe the irreducible representations of the groups Aut(M) for
any finite O-module M of rank two. The main emphasis is on the interaction
between the different groups and their representations. An induction scheme is
developed in order to study the whole family of these groups coherently. The
results obtained depend on the ring O in a very weak manner, mainly through the
degree of the residue field. In particular, a uniform description of the
irreducible representations of GL(2,O/P^k) is obtained, where P is the maximal
ideal of O.Comment: Final version, to appear in Advances in Mathematic
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