1,110 research outputs found
Some results on reducibility of parabolic induction for classical groups
Given a (complex, smooth) irreducible representation of the general
linear group over a non-archimedean local field and an irreducible
supercuspidal representation of a classical group, we show that the
(normalized) parabolic induction is reducible if there
exists in the supercuspidal support of such that
is reducible. In special cases we also give irreducibility
criteria for when the above condition is not satisfied
Relation spaces of hyperplane arrangements and modules defined by graphs of fiber zonotopes
We study the exactness of certain combinatorially defined complexes which
generalize the Orlik-Solomon algebra of a geometric lattice. The main results
pertain to complex reflection arrangements and their restrictions. In
particular, we consider the corresponding relation complexes and give a simple
proof of the -formality of these hyperplane arrangements. As an application,
we are able to bound the Castelnouvo-Mumford regularity of certain modules over
polynomial rings associated to Coxeter arrangements (real reflection
arrangements) and their restrictions. The modules in question are defined using
the relation complex of the Coxeter arrangement and fiber polytopes of the dual
Coxeter zonotope. They generalize the algebra of piecewise polynomial functions
on the original arrangement
Spectral asymptotics for arithmetic quotients of SL(n,R)/SO(n)
In this paper we study the asymptotic distribution of the cuspidal spectrum
of arithmetic quotients of the symmetric space S=SL(n,R)/SO(n). In particular,
we obtain Weyl's law with an estimation on the remainder term. This extends
results of Duistermaat-Kolk-Varadarajan on spectral asymptotics for compact
locally symmetric spaces to this non-compact setting.Comment: 31 page
On an analogue of the Ichino--Ikeda conjecture for Whittaker coefficients on the metaplectic group
In previous papers we formulated an analogue of the Ichino--Ikeda conjectures
for Whittaker--Fourier coefficients of automorphic forms on classical group and
the metaplectic group. In the latter case we reduced the conjecture to a local
identity. In this paper we will prove the local identity in the -adic case,
and hence the global conjecture under simplifying conditions at the archimedean
places.Comment: stylistic changes since last version to appear in Algebra and Number
Theor
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