192,945 research outputs found
Analysis on the minimal representation of O(p,q) -- II. Branching laws
This is a second paper in a series devoted to the minimal unitary
representation of O(p,q).
By explicit methods from conformal geometry of pseudo-Riemannian manifolds,
we find the branching law corresponding to restricting the minimal unitary
representation to natural symmetric subgroups.
In the case of purely discrete spectrum we obtain the full spectrum and give
an explicit Parseval-Plancherel formula, and in the general case we construct
an infinite discrete spectrum.Comment: 27 page
Analysis on the minimal representation of O(p,q) -- I. Realization via conformal geometry
This is the first in a series of papers devoted to an analogue of the
metaplectic representation, namely, the minimal unitary representation of an
indefinite orthogonal group; this representation corresponds to the minimal
nilpotent coadjoint orbit in the philosophy of Kirillov-Kostant.
We begin by applying methods from conformal geometry of pseudo-Riemannian
manifolds to a general construction of an infinite-dimensional representation
of the conformal group on the solution space of the Yamabe equation. By
functoriality of the constructions, we obtain different models of the unitary
representation, as well as giving new proofs of unitarity and irreducibility.
The results in this paper play a basic role in the subsequent papers, where
we give explicit branching formulae, and prove unitarization in the various
models
Parity criterion and Dehn twists for unstabilized Heegaard splittings
We give a parity condition of a Heegaard diagram to show that it is
unstabilized. This improves the result of [5]. As an application, we construct
unstabilized Heegaard splittings by Dehn twists on any given Heegaard
splitting.Comment: 10 pages, 6 figure
The magnetic behavior of Li2MO3 (M=Mn, Ru and Ir) and Li2(Mn1-xRux)O3
The present study summerizes magnetic and Mossbauer measurements on ceramic
Li2MO3 M= Mn, Ru and Ir and the mixed Li2(Mn1-xRux)O3 materials, which show
many of the features reflecting to antiferromagnetic ordering or to existence
of paramagnetic states. Li2IrO3 and Li2RuO3 are paramagnetic down to 5 K.
Li2(Mn1-xRux)O3 compounds are antiferromagnetically ordered at TN = 48 K for
x=0. TN decreases as the Ru content increases and, for x=0.8, TN =34 K.Comment: accepted to Physica
New RG-invariants of Soft Supersymmetry Breaking Parameters
We study new renormalization-group invariant quantities of soft supersymmetry
breaking parameters other than the ratio of gaugino mass to gauge coupling
squared by using the spurion method. The obtained invariants are useful to
probe supersymmetry breaking and mu-term generation mechanisms at high-energy
scale. We also discuss the convergence behavior of fixed points of
supersymmetry breaking parameters.Comment: 9 page
Heterotic string backgrounds and CP violation
In the framework of orbifolds, we discuss effects of heterotic string
backgrounds including discrete Wilson lines on the Yukawa matrices and their
connection to CP violation.Comment: 12 pages, latex, no figur
Rolling in the Modulated Reheating Scenario
In the modulated reheating scenario, the field that drives inflation has a
spatially varying decay rate, and the resulting inhomogeneous reheating process
generates adiabatic perturbations. We examine the statistical properties of the
density perturbations generated in this scenario. Unlike earlier analyses, we
include the dynamics of the field that determines the inflaton decay rate. We
show that the dynamics of this modulus field can significantly alter the
amplitude of the power spectrum and the bispectrum, even if the modulus field
has a simple potential and its effective mass is smaller than the Hubble rate.
In some cases, the evolution of the modulus amplifies the non-Gaussianity of
the perturbations to levels that are excluded by recent observations of the
cosmic microwave background. Therefore, a proper treatment of the modulus
dynamics is required to accurately calculate the statistical properties of the
perturbations generated by modulated reheating.Comment: 27 pages, 11 figures: minor changes made to match version in JCA
Quark masses and mixing angles in heterotic orbifold models
We study systematically the possibility for realizing realistic values of
quark mass ratios and and the mixing angle by
using only renormalizable Yukawa couplings derived from heterotic orbifold
models. We assume one pair of up and down sector Higgs fields. We show
realistic examples including hierarchical and democratic forms of Yukawa
matrices.Comment: 16 pages, late
Sum rules in the superpartner spectrum of the minimal supersymmetric standard model
Assuming that the string inspired, universal sum rules for soft
supersymmetry-breaking terms, which have been recently found both in a wide
class of four-dimensional superstrings and in supersymmertic gauge-Yukawa
unified gauge models, are satisfied above and at the grand unification scale,
we investigate theirlow energy consequences and derive sum rules in the
superpartner spectrum of the minimal supersymmetric standard model.Comment: 10 pages, LaTex 4 figure
Finite multiplicity theorems for induction and restriction
We find upper and lower bounds of the multiplicities of irreducible
admissible representations of a semisimple Lie group occurring in the
induced representations from irreducible representations
of a closed subgroup .
As corollaries, we establish geometric criteria for finiteness of the
dimension of (induction) and of
(restriction) by means of the real flag variety , and discover that
uniform boundedness property of these multiplicities is independent of real
forms and characterized by means of the complex flag variety.Comment: to appear in Advances in Mathematic
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