95 research outputs found
Local monotonicity of Riemannian and Finsler volume with respect to boundary distances
We show that the volume of a simple Riemannian metric on is locally
monotone with respect to its boundary distance function. Namely if is a
simple metric on and is sufficiently close to and induces
boundary distances greater or equal to those of , then . Furthermore, the same holds for Finsler metrics and the
Holmes--Thompson definition of volume. As an application, we give a new proof
of the injectivity of the geodesic ray transform for a simple Finsler metric.Comment: 13 pages, v3: minor corrections and clarifications, to appear in
Geometriae Dedicat
Generalized Bernstein--Reznikov integrals
We find a closed formula for the triple integral on spheres in
whose kernel is
given by powers of the standard symplectic form. This gives a new proof to the
Bernstein--Reznikov integral formula in the case. Our method also applies
for linear and conformal structures
Special Reduced Multiplets and Minimal Representations for SO(p,q)
Using our previous results on the systematic construction of invariant
differential operators for non-compact semisimple Lie groups we classify the
special reduced multiplets and minimal representations in the case of SO(p,q).Comment: 26 pages, 11 figures, to appear in the Proceedings of the X
International Workshop "Lie Theory and Its Applications in Physics}, (Varna,
Bulgaria, June 2013), "Springer Proceedings in Mathematics and Statistics",
Vol. 11
Invariant Differential Operators for Non-Compact Lie Groups: the Sp(n,R) Case
In the present paper we continue the project of systematic construction of
invariant differential operators on the example of the non-compact algebras
sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the
fact that they belong to a narrow class of algebras, which we call 'conformal
Lie algebras', which have very similar properties to the conformal algebras of
Minkowski space-time. We give the main multiplets and the main reduced
multiplets of indecomposable elementary representations for n=6, including the
necessary data for all relevant invariant differential operators. In fact, this
gives by reduction also the cases for n<6, since the main multiplet for fixed n
coincides with one reduced case for n+1.Comment: Latex2e, 27 pages, 8 figures. arXiv admin note: substantial text
overlap with arXiv:0812.2690, arXiv:0812.265
On representation theory of affine Hecke algebras of type B
Ariki's and Grojnowski's approach to the representation theory of affine
Hecke algebras of type is applied to type with unequal parameters to
obtain -- under certain restrictions on the eigenvalues of the lattice
operators -- analogous multiplicity-one results and a classification of
irreducibles with partial branching rules as in type .Comment: to appear in Algebras and Representation theor
The nil Hecke ring and singularity of Schubert varieties
We give a criterion for smoothness of a point in any Schubert variety in any
G/B in terms of the nil Hecke ring.Comment: AMSTE
The classification of irreducible admissible mod p representations of a p-adic GL_n
Let F be a finite extension of Q_p. Using the mod p Satake transform, we
define what it means for an irreducible admissible smooth representation of an
F-split p-adic reductive group over \bar F_p to be supersingular. We then give
the classification of irreducible admissible smooth GL_n(F)-representations
over \bar F_p in terms of supersingular representations. As a consequence we
deduce that supersingular is the same as supercuspidal. These results
generalise the work of Barthel-Livne for n = 2. For general split reductive
groups we obtain similar results under stronger hypotheses.Comment: 55 pages, to appear in Inventiones Mathematica
Super duality and irreducible characters of ortho-symplectic Lie superalgebras
We formulate and establish a super duality which connects parabolic
categories between the ortho-symplectic Lie superalgebras and classical Lie
algebras of types. This provides a complete and conceptual solution of
the irreducible character problem for the ortho-symplectic Lie superalgebras in
a parabolic category , which includes all finite-dimensional irreducible
modules, in terms of classical Kazhdan-Lusztig polynomials.Comment: 30 pages, Section 5 rewritten and shortene
On limit multiplicites of discrete series representations in spaces of automorphic forms
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46616/1/222_2005_Article_BF01388963.pd
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