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 $(p,q)$-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 $G = P_1 \cup ...\cup P_N$ into disjoint subsets and a bijection between $\{P_1,...,P_N\}$ and the sectors $\{S_1,...,S_N\}$ of the $(p,q)$-minimal model such that the fusion rules $S_i * S_j = \sum_k D(S_i,S_j,S_k) S_k$ correspond to $P_i * P_j = \sum_{k\in T(i,j)} P_k$ where $T(i,j) = \{k|\exists a\in P_i,\exists b\in P_j, a+b\in P_k\}$.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