290,517 research outputs found
Inducing -partial characters with a given vertex
Let be a solvable group. Let be a prime and let be a -subgroup
of a subgroup . Suppose \phi \in \ibr G. If either is odd or , we prove that the number of Brauer characters of inducing with
vertex is at most |\norm GQ: \norm VQ|
A lower bound for the height of a rational function at -unit points
Let be a finitely generated subgroup of the multiplicative group
\G_m^2(\bar{Q}). Let p(X,Y),q(X,Y)\in\bat{Q} be two coprime polynomials not
both vanishing at ; let . We prove that, for all
outside a proper Zariski closed subset of , the height
of verifies . As a consequence, we deduce upper bounds for (a generalized
notion of) the g.c.d. of for running over .Comment: Plain TeX 18 pages. Version 2; minor changes. To appear on
Monatshefte fuer Mathemati
A new construction of homogeneous quaternionic manifolds and related geometric structures
Let V be the pseudo-Euclidean vector space of signature (p,q), p>2 and W a
module over the even Clifford algebra Cl^0 (V). A homogeneous quaternionic
manifold (M,Q) is constructed for any spin(V)-equivariant linear map \Pi :
\wedge^2 W \to V. If the skew symmetric vector valued bilinear form \Pi is
nondegenerate then (M,Q) is endowed with a canonical pseudo-Riemannian metric g
such that (M,Q,g) is a homogeneous quaternionic pseudo-K\"ahler manifold.
The construction is shown to have a natural mirror in the category of
supermanifolds. In fact, for any spin(V)-equivariant linear map \Pi : Sym^2 W
\to V a homogeneous quaternionic supermanifold (M,Q) is constructed and,
moreover, a homogeneous quaternionic pseudo-K\"ahler supermanifold (M,Q,g) if
the symmetric vector valued bilinear form \Pi is nondegenerate.Comment: to appear in the Memoirs of the AMS, 81 pages, Latex source fil
A uniform classification of discrete series representations of affine Hecke algebras
We give a new and independent parameterization of the set of discrete series
characters of an affine Hecke algebra , in terms of a
canonically defined basis of a certain lattice of virtual
elliptic characters of the underlying (extended) affine Weyl group. This
classification applies to all semisimple affine Hecke algebras ,
and to all , where denotes the vector
group of positive real (possibly unequal) Hecke parameters for .
By analytic Dirac induction we define for each a
continuous (in the sense of [OS2]) family
,
such that (for
some ) is an irreducible discrete series
character of . Here
is a finite union of hyperplanes in
.
In the non-simply laced cases we show that the families of virtual discrete
series characters are piecewise rational
in the parameters . Remarkably, the formal degree of
in such piecewise rational family turns
out to be rational. This implies that for each there
exists a universal rational constant determining the formal degree in the
family of discrete series characters
. We will compute
the canonical constants , and the signs . For
certain geometric parameters we will provide the comparison with the
Kazhdan-Lusztig-Langlands classification.Comment: 31 pages, 2 table
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