2,521 research outputs found
On irreducible representations of the exotic conformal Galilei algebra
We investigate the representations of the exotic conformal Galilei algebra.
This is done by explicitly constructing all singular vectors within the Verma
modules, and then deducing irreducibility of the associated highest weight
quotient modules. A resulting classification of infinite dimensional
irreducible modules is presented.Comment: 11 pages, added 6 references and conclusing remark
Highest weight representations and Kac determinants for a class of conformal Galilei algebras with central extension
We investigate the representations of a class of conformal Galilei algebras
in one spatial dimension with central extension. This is done by explicitly
constructing all singular vectors within the Verma modules, proving their
completeness and then deducing irreducibility of the associated highest weight
quotient modules. A resulting classification of infinite dimensional
irreducible modules is presented. It is also shown that a formula for the Kac
determinant is deduced from our construction of singular vectors. Thus we prove
a conjecture of Dobrev, Doebner and Mrugalla for the case of the Schrodinger
algebra.Comment: 24 page
Laughlin states on the sphere as representations of Uq(sl(2))
We discuss quantum algebraic structures of the systems of electrons or
quasiparticles on a sphere of which center a magnetic monople is located on. We
verify that the deformation parameter is related to the filling ratio of the
particles in each case.Comment: 8 pages, Late
generalizations of superconformal Galilei algebras and their representations
We introduce two classes of novel color superalgebras of grading. This is done by realizing members of each in the
universal enveloping algebra of the supersymmetric extension of
the conformal Galilei algebra. This allows us to upgrade any representation of
the super conformal Galilei algebras to a representation of the graded algebra. As an example, boson-fermion Fock space
representation of one class is given. We also provide a vector field
realization of members of the other class by using a generalization of the
Grassmann calculus to graded setting.Comment: 17 pages, no figur
Lowest weight representations of super Schrodinger algebras in low dimensional spacetime
We investigate the lowest weight representations of the super Schrodinger
algebras introduced by Duval and Horvathy. This is done by the same procedure
as the semisimple Lie algebras. Namely, all singular vectors within the Verma
modules are constructed explicitly then irreducibility of the associated
quotient modules is studied again by the use of singular vectors. We present
the classification of irreducible Verma modules for the super Schrodinger
algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.Comment: 10pages, talk given at GROUP28 conference New Castle 26-30th July
2010, reference adde
Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space
Lowest weight modules, in particular, Verma modules over the N = 1,2 super
Schrodinger algebras in (1+1) dimensional spacetime are investigated. The
reducibility of the Verma modules is analyzed via explicitly constructed
singular vectors. The classification of the irreducible lowest weight modules
is given for both massive and massless representations. A vector field
realization of the N = 1, 2 super Schrodinger algebras is also presented.Comment: 19 pages, no figur
Generalized Arcsine Law and Stable Law in an Infinite Measure Dynamical System
Limit theorems for the time average of some observation functions in an
infinite measure dynamical system are studied. It is known that intermittent
phenomena, such as the Rayleigh-Benard convection and Belousov-Zhabotinsky
reaction, are described by infinite measure dynamical systems.We show that the
time average of the observation function which is not the function,
whose average with respect to the invariant measure is finite, converges to
the generalized arcsine distribution. This result leads to the novel view that
the correlation function is intrinsically random and does not decay. Moreover,
it is also numerically shown that the time average of the observation function
converges to the stable distribution when the observation function has the
infinite mean.Comment: 8 pages, 8 figure
Regularized Renormalization Group Reduction of Symplectic Map
By means of the perturbative renormalization group method, we study a
long-time behaviour of some symplectic discrete maps near elliptic and
hyperbolic fixed points. It is shown that a naive renormalization group (RG)
map breaks the symplectic symmetry and fails to describe a long-time behaviour.
In order to preserve the symplectic symmetry, we present a regularization
procedure, which gives a regularized symplectic RG map describing an
approximate long-time behaviour succesfully
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