85 research outputs found
A Laplace operator and harmonics on the quantum complex vector space
The aim of this paper is to study the q-Laplace operator and q-harmonic
polynomials on the quantum complex vector space generated by z_i,w_i,
i=1,2,...,n, on which the quantum group GL_q(n) (or U_q(n)) acts. The
q-harmonic polynomials are defined as solutions of the equation Delta_qp=0,
where p is a polynomial in z_i,w_i, i=1,2,...,n, and the q-Laplace operator
Delta_q is determined in terms of q-derivatives. The q-Laplace operator Delta_q
commutes with the action of GL_q(n). The projector H_{m,m'}: A_{m,m'} -->
H_{m,m'} is constructed, where A_{m,m'} and H_{m,m'} are the spaces of
homogeneous (of degree m in z_i and of degree m' in w_i) polynomials and
homogeneous q-harmonic polynomials, respectively. By using these projectors, a
q-analogue of the classical zonal spherical and associated spherical harmonics
are constructed. They constitute an orthogonal basis of H_{m,m'}. A q-analogue
of separation of variables is given. The quantum algebra U_q(gl_n), acting on
H_{m,m'}, determines an irreducible representation of U_q(gl_n). This action is
explicitly constructed. The results of the paper lead to the dual pair
(U_q(sl_2), U_q(gl_n)) of quantum algebras.Comment: 26 pages, LaTe
Representations of the q-deformed algebra U'_q(so_4)
We study the nonstandard -deformation of the universal
enveloping algebra obtained by deforming the defining relations
for skew-symmetric generators of . This algebra is used in
quantum gravity and algebraic topology. We construct a homomorphism of
to the certain nontrivial extension of the Drinfeld--Jimbo
quantum algebra and show that this homomorphism
is an isomorphism. By using this homomorphism we construct irreducible finite
dimensional representations of the classical type and of the nonclassical type
for the algebra . It is proved that for not a root of
unity each irreducible finite dimensional representation of
is equivalent to one of these representations. We prove that every finite
dimensional representation of for not a root of unity is
completely reducible. It is shown how to construct (by using the homomorphism
) tensor products of irreducible representations of .
(Note that no Hopf algebra structure is known for .) These
tensor products are decomposed into irreducible constituents.Comment: 28 pages, LaTe
Symmetries and invariants of twisted quantum algebras and associated Poisson algebras
We construct an action of the braid group B_N on the twisted quantized
enveloping algebra U'_q(o_N) where the elements of B_N act as automorphisms. In
the classical limit q -> 1 we recover the action of B_N on the polynomial
functions on the space of upper triangular matrices with ones on the diagonal.
The action preserves the Poisson bracket on the space of polynomials which was
introduced by Nelson and Regge in their study of quantum gravity and
re-discovered in the mathematical literature. Furthermore, we construct a
Poisson bracket on the space of polynomials associated with another twisted
quantized enveloping algebra U'_q(sp_{2n}). We use the Casimir elements of both
twisted quantized enveloping algebras to re-produce some well-known and
construct some new polynomial invariants of the corresponding Poisson algebras.Comment: 29 pages, more references adde
Painleve IV and degenerate Gaussian Unitary Ensembles
We consider those Gaussian Unitary Ensembles where the eigenvalues have
prescribed multiplicities, and obtain joint probability density for the
eigenvalues. In the simplest case where there is only one multiple eigenvalue
t, this leads to orthogonal polynomials with the Hermite weight perturbed by a
factor that has a multiple zero at t. We show through a pair of ladder
operators, that the diagonal recurrence coefficients satisfy a particular
Painleve IV equation for any real multiplicity. If the multiplicity is even
they are expressed in terms of the generalized Hermite polynomials, with t as
the independent variable.Comment: 17 page
Search for H hypernucleus by the Li reaction at = 1.2 GeV/
We have carried out an experiment to search for a neutron-rich hypernucleus,
H, by the Li() reaction at =1.2
GeV/. The obtained missing mass spectrum with an estimated energy resolution
of 3.2 MeV (FWHM) showed no peak structure corresponding to the H
hypernucleus neither below nor above the H particle decay
threshold. An upper limit of the production cross section for the bound
H hypernucleus was estimated to be 1.2 nb/sr at 90% confidence
level.Comment: 6 pages, 5 figures, published versio
Search for the pentaquark via the reaction at 1.92 GeV/
The pentaquark baryon was searched for via the
reaction in a missing-mass resolution of 1.4 MeV/(FWHM) at J-PARC.
meson beams were incident on the liquid hydrogen target with the beam momentum
of 1.92 GeV/. No peak structure corresponding to the mass was
observed. The upper limit of the production cross section averaged over the
scattering angle of 2 to 15 in the laboratory frame was
obtained to be 0.26 b/sr in the mass region of 1.511.55 GeV/.The
upper limit of the decay width using the effective Lagrangian
approach was obtained to be 0.72 MeV/ and 3.1 MeV/ for
and , respectively.Comment: 5 pages, 3 figures, 1 tabl
Beam and SKS spectrometers at the K1.8 beam line
High-resolution spectrometers for both incident beams and scattered particles have been constructed at the K1.8 beam line of the Hadron Experimental Facility at J-PARC. A point-to-point optics is realized between the entrance and exit of QQDQQ magnets for the beam spectrometer. Fine-pitch wire chamber trackers and hodoscope counters are installed in the beam spectrometer to accept a high rate beam up to 107 Hz. The superconducting kaon spectrometer for scattered particles was transferred from KEK with modifications to the cryogenic system and detectors. A missing-mass resolution of 1.9 ± 0.1 MeV/c2 (FWHM) was achieved for the ∑ peaks of (π±, K+) reactions on a proton target in the first physics run of E19 in 2010
Search for the pentaquark at J-PARC
We have been searching for the Θ^+ pentaquark via the π^−p→K^−X reaction at the J-PARC hadron facility. No peak structure was observed in the missing mass spectrum obtained at 1.92 GeV/c beam momentum. The upper limit for the production cross section averaged over the scattering angle from 2° to 15° in the laboratory frame was derived to be 0.26 μb/sr. In order to make a more stringent constraint we have also performed a measurement at 2.0 GeV/c. Present analysis status of this new data is reported
Pole position of measured in reactions
We measured a set of , , and
invariant mass spectra below and above the mass
threshold in -induced reactions on deuteron. We deduced the -wave
and scattering
amplitudes in the isospin 0 channel in the framework of a and
coupled channel. We find that a resonance pole corresponding to
is located at 1417.7(fitting
errors)(systematic errors) + (fitting
errors)(systematic errors)] MeV/, closer to the
mass threshold than the value determined by the Particle Data Group.Comment: 8 pages, 5 figure
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