3,051 research outputs found
Fusion Rules for Affine Kac-Moody Algebras
This is an expository introduction to fusion rules for affine Kac-Moody
algebras, with major focus on the algorithmic aspects of their computation and
the relationship with tensor product decompositions. Many explicit examples are
included with figures illustrating the rank 2 cases. New results relating
fusion coefficients to tensor product coefficients are proved, and a conjecture
is given which shows that the Frenkel-Zhu affine fusion rule theorem can be
seen as a beautiful generalization of the Parasarathy-Ranga Rao-Varadarajan
tensor product theorem. Previous work of the author and collaborators on a
different approach to fusion rules from elementary group theory is also
explained.Comment: 43 pp, LateX, 18 postscript figures. Paper for my talk at the
Ramanujan International Symposium on Kac-Moody Lie Algebras and Applications,
ISKMAA-2002, Jan. 28-31, 2002, Chennai, India. Important references and
comments added. Final version accepted for publication. Also available from
ftp://ftp.math.binghamton.edu/pub/alex/Madras_Paper_Latex.ps.g
A new perspective on the Frenkel-Zhu fusion rule theorem
In this paper we prove a formula for fusion coefficients of affine Kac-Moody
algebras first conjectured by Walton [Wal2], and rediscovered in [Fe]. It is a
reformulation of the Frenkel-Zhu affine fusion rule theorem [FZ], written so
that it can be seen as a beautiful generalization of the classical
Parasarathy-Ranga Rao-Varadarajan tensor product theorem [PRV].Comment: 19 pages, no figures, uses conm-p-l.cls style fil
Minimal model fusion rules from 2-groups
The fusion rules for the -minimal model representations of the
Virasoro algebra are shown to come from the group G = \boZ_2^{p+q-5} in the
following manner. There is a partition into disjoint
subsets and a bijection between and the sectors
of the -minimal model such that the fusion rules correspond to where .Comment: 8 pages, amstex, v2.1, uses fonts msam, msbm, no figures, tables
constructed using macros: cellular and related files are included. This paper
will be submitted to Communications in Math. Physics. A compressed dvi file
is available at ftp://math.binghamton.edu/pub/alex/fusionrules.dvi.Z , and
compressed postscript at ftp://math.binghamton.edu/pub/alex/fusionrules.ps.
Investigation of the reinforcement of ductile metals with strong, high modulus discontinuous brittle fibers Quarterly report
Factors affecting reinforcement of aluminum with boron carbide whisker
Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions
We consider chaotic billiards in d dimensions, and study the matrix elements
M_{nm} corresponding to general deformations of the boundary. We analyze the
dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical
considerations. This relates to an estimate of the energy dissipation rate when
the deformation is periodic at frequency \omega. We show that for dilations and
translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0,
for rotations like \omega^2, whereas for generic deformations it goes to a
constant. Such special cases lead to quasi-orthogonality of the eigenstates on
the boundary.Comment: 4 pages, 3 figure
Study of the growth parameters involved in synthesizing boron carbide filaments Second quarterly report
Growth parameters in synthesis of boron carbide whisker
secCl is a cys-loop ion channel necessary for the chloride conductance that mediates hormone-induced fluid secretion in Drosophila
Organisms use circulating diuretic hormones to control water balance (osmolarity), thereby avoiding dehydration and managing excretion of waste products. The hormones act through G-protein-coupled receptors to activate second messenger systems that in turn control the permeability of secretory epithelia to ions like chloride. In insects, the chloride channel mediating the effects of diuretic hormones was unknown. Surprisingly, we find a pentameric, cys-loop chloride channel, a type of channel normally associated with neurotransmission, mediating hormone-induced transepithelial chloride conductance. This discovery is important because: 1) it describes an unexpected role for pentameric receptors in the membrane permeability of secretory epithelial cells, and 2) it suggests that neurotransmitter-gated ion channels may have evolved from channels involved in secretion
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