52,756 research outputs found
An expansion of the Jones representation of genus 2 and the Torelli group
We study the algebraic property of the representation of the mapping class
group of a closed oriented surface of genus 2 constructed by VFR Jones [Annals
of Math. 126 (1987) 335-388]. It arises from the Iwahori-Hecke algebra
representations of Artin's braid group of 6 strings, and is defined over
integral Laurent polynomials Z[t, t^{-1}]. We substitute the parameter t with
-e^{h}, and then expand the powers e^h in their Taylor series. This expansion
naturally induces a filtration on the Torelli group which is coarser than its
lower central series. We present some results on the structure of the
associated graded quotients, which include that the second Johnson homomorphism
factors through the representation. As an application, we also discuss the
relation with the Casson invariant of homology 3-spheres.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-3.abs.htm
Rapidity Dependence of HBT radii based on a hydrodynamical model
We calculate two-pion correlation functions at finite rapidities based on a
hydrodynamical model which does not assume explicit boost invariance along the
collision axis. Extracting the HBT radii through fits in both
Cartesian and Yano-Koonin-Podgoretski\u{\i} parametrizations, we compare them
with the experimental results obtained by the PHOBOS. Based on the results, we
discuss longitudinal expansion dynamics.Comment: 8 pages, 10 figures, talk given at II Workshop on Particle
Correlation and Femtoscopy (WPCF 2006), Sep 9-11, Sao Paulo, Brazil. Revised
version to be published in Braz.J.Phy
A Connection Formula of the Hahn-Exton -Bessel Function
We show a connection formula of the Hahn-Exton -Bessel function around the
origin and the infinity. We introduce the -Borel transformation and the
-Laplace transformation following C. Zhang to obtain the connection formula.
We consider the limit of the connection formula
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