6,427 research outputs found
Modular realizations of hyperbolic Weyl groups
We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group
Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e
We show that the maximal extension sl(2) times psl(2|2) times C3 of the
sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple
superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the
corresponding q-deformed Hopf algebra and its universal R-matrix by means of
contraction. We make the curious observation that the above algebra is related
to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a
novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our
construction also provides a concise exact expression for its universal
R-matrix.Comment: 25 page
Modular realizations of hyperbolic Weyl groups
We study the recently discovered isomorphisms between hyperbolic Weyl groups and unfamiliar modular groups. These modular groups are defined over integer domains in normed division algebras, and we focus on the cases involving quaternions and octonions. We outline how to construct and analyse automorphic forms for these groups; their structure depends on the underlying arithmetic properties of the integer domains. We also give a new realization of the Weyl group W(E8) in terms of unit octavians and their automorphism group
Evidence for the PSL(22) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
In this paper I revise arguments in favour of the PSL(22)
Wess-Zumino-Novikov-Witten (WZNW) model as a theory of the plateau transition
in Integer Quantum Hall effect. I show that all available numerical data
(including the correlation length exponent ) are consistent with the
predictions of such WZNW model with the level .Comment: 11 pages, no figure
Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms
A unified treatment is given of low-weight modular forms on \Gamma_0(N),
N=2,3,4, that have Eisenstein series representations. For each N, certain
weight-1 forms are shown to satisfy a coupled system of nonlinear differential
equations, which yields a single nonlinear third-order equation, called a
generalized Chazy equation. As byproducts, a table of divisor function and
theta identities is generated by means of q-expansions, and a transformation
law under \Gamma_0(4) for the second complete elliptic integral is derived.
More generally, it is shown how Picard-Fuchs equations of triangle subgroups of
PSL(2,R) which are hypergeometric equations, yield systems of nonlinear
equations for weight-1 forms, and generalized Chazy equations. Each triangle
group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic
- …