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

Passive Scalars and Three-Dimensional Liouvillian Maps

Global aspects of the motion of passive scalars in time-dependent incompressible fluid flows are well described by volume-preserving (Liouvillian) three-dimensional maps. In this paper the possible invariant structures in Liouvillian maps and the two most interesting nearly-integrable cases are investigated. In addition, the fundamental role of invariant lines in organizing the dynamics of this type of system is exposed. Bifurcations involving the destruction of some invariant lines and tubes and the creation of new ones are described in detail.Comment: 18 pages, plain TeX, appears in Physica D, 76, 22-33, 1994. (Lack of figures in original submission corrected in this new upload.

The War on Newton

No abstract

Radial furnace shows promise for growing straight boron carbide whiskers

Radial furnace, with a long graphite vaporization tube, maintains a uniform thermal gradient, favoring the growth of straight boron carbide whiskers. This concept seems to offer potential for both the quality and yield of whiskers

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

E11 as E10 representation at low levels

The Lorentzian Kac-Moody algebra E11, obtained by doubly overextending the compact E8, is decomposed into representations of its canonical hyperbolic E10 subalgebra. Whereas the appearing representations at levels 0 and 1 are known on general grounds, higher level representations can currently only be obtained by recursive methods. We present the results of such an analysis up to height 120 in E11 which comprises representations on the first five levels. The algorithms used are a combination of Weyl orbit methods and standard methods based on the Peterson and Freudenthal formulae. In the appendices we give all multiplicities of E10 occuring up to height 340 and for E11 up to height 240.Comment: 1+32 pages, 1 figure, LaTeX2e, uses longtable package;v2: corrected typo in formula and added references, results unchanged;v3: corrected reference [26

The 3-state Potts model and Rogers-Ramanujan series

We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic $A_2^{(2)}$-modules, previously discovered by the first author in [F]. The key new ingredients are $(5,6)$ Virasoro minimal models and twisted modules for the Zamolodchikov \WW_3-algebra.Comment: 20 pages, published in CEJ

Quantum Ergodicity and Localization in Conservative Systems: the Wigner Band Random Matrix Model

First theoretical and numerical results on the global structure of the energy shell, the Green function spectra and the eigenfunctions, both localized and ergodic, in a generic conservative quantum system are presented. In case of quantum localization the eigenfunctions are shown to be typically narrow and solid, with centers randomly scattered within the semicircle energy shell while the Green function spectral density (local spectral density of states) is extended over the whole shell, but sparse.Comment: 4 pages in RevTex and 4 Postscript figures; presented to Phys. Lett.