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

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

Heterotic string backgrounds and CP violation

In the framework of $Z_N$ 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

Quark masses and mixing angles in heterotic orbifold models

We study systematically the possibility for realizing realistic values of quark mass ratios $m_c/m_t$ and $m_s/m_b$ and the mixing angle $V_{cb}$ 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 $\pi$ of a semisimple Lie group $G$ occurring in the induced representations $Ind_H^G\tau$ from irreducible representations $\tau$ of a closed subgroup $H$. As corollaries, we establish geometric criteria for finiteness of the dimension of $Hom_G(\pi,Ind_H^G \tau)$ (induction) and of $Hom_H(\pi|_H,\tau)$ (restriction) by means of the real flag variety $G/P$, 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