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

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

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

Entropy Burst from Parabolic Potentials

The change of the energy of ground state is investigated in a thermodynamical process by using the model described by one-dimensional harmonic oscillator + two-dimensional isotropic parabolic potential barrier such as $V(x,y,z)=m\omega^2 x^2/2 -m\gamma^2 (y^2+z^2)/2$. In the process where two independent many-particle systems suddenly touch with each other, it is shown that the lowest energy after the interaction can possibly be smaller than that before the interaction and then the entropy burst can occur.Comment: 6 pages, AmS-LaTeX, 1 figur