49,429 research outputs found

### Vector-valued covariant differential operators for the M\"obius transformation

We obtain a family of functional identities satisfied by vector-valued
functions of two variables and their geometric inversions. For this we
introduce particular differential operators of arbitrary order attached to
Gegenbauer polynomials. These differential operators are symmetry breaking for
the pair of Lie groups $(SL(2,\mathbb C), SL(2,\mathbb R))$ that arise from
conformal geometry.Comment: To appear in Springer Proceedings in Mathematics and Statistic

### Restrictions of generalized Verma modules to symmetric pairs

We initiate a new line of investigation on branching problems for generalized
Verma modules with respect to complex reductive symmetric pairs (g,k). Here we
note that Verma modules of g may not contain any simple module when restricted
to a reductive subalgebra k in general.
In this article, using the geometry of K_C orbits on the generalized flag
variety G_C/P_C, we give a necessary and sufficient condition on the triple
(g,k, p) such that the restriction X|_k always contains simple k-modules for
any g-module $X$ lying in the parabolic BGG category O^p attached to a
parabolic subalgebra p of g.
Formulas are derived for the Gelfand-Kirillov dimension of any simple
k-module occurring in a simple generalized Verma module of g. We then prove
that the restriction X|_k is multiplicity-free for any generic g-module X \in O
if and only if (g,k) is isomorphic to a direct sum of (A_n,A_{n-1}), (B_n,D_n),
or (D_{n+1},B_n). We also see that the restriction X|_k is multiplicity-free
for any symmetric pair (g, k) and any parabolic subalgebra p with abelian
nilradical and for any generic g-module X \in O^p. Explicit branching laws are
also presented.Comment: 31 pages, To appear in Transformation Group

### Minimal String Unification and Yukawa Couplings in Orbifold Models

We study the minimal supersymmetric standard model derived from $Z_N \times
Z_M$ orbifold models. Moduli dependent threshold corrections of the gauge
couplings are investigated to explain the measured values of the coupling
constants. Also we study Yukawa couplings of the models. We find that the $Z_2
\times Z_6'$, $Z_2\times Z_6$, $Z_3 \times Z_6$ and $Z_6 \times Z_6$ orbifold
models have the possibility to derive Yukawa couplings for the second and third
generations as well as the measured gauge coupling constants. Allowed models
are shown explicitly by combinations of modular weights for the matter fields.Comment: 26 pages, KANAZAWA-94-10, Latex fil

### Hidden gauge structure and derivation of microcanonical ensemble theory of bosons from quantum principles

Microcanonical ensemble theory of bosons is derived from quantum mechanics by
making use of a hidden gauge structure. The relative phase interaction
associated with this gauge structure, described by the Pegg-Barnett formalism,
is shown to lead to perfect decoherence in the thermodynamics limit and the
principle of equal a priori probability, simultaneously.Comment: 10 page

### Global analysis by hidden symmetry

Hidden symmetry of a G'-space X is defined by an extension of the G'-action
on X to that of a group G containing G' as a subgroup. In this setting, we
study the relationship between the three objects:
(A) global analysis on X by using representations of G (hidden symmetry);
(B) global analysis on X by using representations of G';
(C) branching laws of representations of G when restricted to the subgroup
G'.
We explain a trick which transfers results for finite-dimensional
representations in the compact setting to those for infinite-dimensional
representations in the noncompact setting when $X_C$ is $G_C$-spherical.
Applications to branching problems of unitary representations, and to spectral
analysis on pseudo-Riemannian locally symmetric spaces are also discussed.Comment: Special volume in honor of Roger Howe on the occasion of his 70th
birthda

### Quantum Deformation of igl(n) Algebra on Quantum Space

We study quantum deformed $gl(n)$ and $igl(n)$ algebras on a quantum space
discussing multi-parametric extension. We realize elements of deformed $gl(n)$
and $igl(n)$ algebras by a quantum fermionic space. We investigate a map
between deformed $igl(2)$ algebras of our basis and other basis.Comment: 14 pages, Latex, version published in Mod. Phys. Lett.

### Fine-tuning in gauge mediated supersymmetry breaking models and induced top Yukawa coupling

It is shown that fine-tuning of the Higgs parameters stronger than a few % is
required at the best in the models with gauge mediated supersymmetry breaking.
With the aim of solving this problem, we consider a new type of models in which
the top Yukawa coupling is induced at TeV scale through mass mixing with
unknown matter fields. Then it is found that the fine-tuning problem can be
eliminated essentially. We discuss some phenomenological features of this model
and also consider the extension to the next-to-minimal models.Comment: 14 pages, 9 Postscript figures, uses revtex4.sty, Some comments and a
reference added, to appear in Phys. Rev.

### Supersymmetric Particle Production at HERA

In the framework of the minimal supersymmetric standard model and the
$R$-parity breaking model, we investigate various production processes of the
supersymmetric partner at HERA energies. Our emphasis is paid upon the scalar
top quark, the partner of top quark, characterized by its lighter mass than the
top quark and other scalar quarks in a model. We propose experimentally
feasible approaches to search for clean signals of the stop from either its
production or decay processes.Comment: 30 pages, LaTeX, 21 figures available upon reques

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