Alex J. Feingold

A hyperbolic Kac-Moody algebra and the theory of Siegel modular forms of genus 2

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Tensor products of certain modules for the generalized cartan matrix lie algebra

The outer multiplicites of tensor product decompositions are computed for the smallest Euclidean Kac-Moody Lie algebra when one of the tensor factors is a fundamental module or the p-module. Some combinatorial identities are obtained.

Zones of uniform decomposition in tensor products

Let Vx be a finite dimensional irreducible module for a complex semisimple Lie algebra. It is shown that the decomposition of tensor products Vx ® Vr for all dominant integral weights t may be derived from those for a finite set of such r. An explicit choice of such a finite set (depending on X) is given.

A New Perspective on the Frenkel-Zhu Fusion Rule Theorem

Abstract In this paper we prove a formula for fusion coefficients of affine Kac–Moody algebras first conjectured by Walton [M.A. Walton, Tensor products and fusion rules, Canad. J. Phys. 72 (1994) 527–536], and rediscovered by Feingold [A. Feingold, Fusion rules for affine Kac–Moody algebras, in: N. Sthanumoorthy, Kailash Misra (Eds.), Kac–Moody Lie Algebras and Related Topics, Ramanujan International Symposium on Kac–Moody Algebras and Applications, Jan. 28–31, 2002, Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, India, in: Contemp. Math., vol. 343, American Mathematical Society, Providence, RI, 2004, pp. 53–96]. It is a reformulation of the Frenkel–Zhu affine fusion rule theorem [I.B. Frenkel, Y. Zhu, Vertex operator algebras associated to representations of affine and Virasoro algebras, Duke Math. J. 66 (1992) 123–168], written so that it can be seen as a beautiful generalization of the classical Parthasarathy–Ranga Rao–Varadarajan tensor product theorem [K.R. Parthasarathy, R. Ranga Rao, V.S. Varadarajan, Representations of complex semi-simple Lie groups and Lie algebras, Ann. of Math. (2) 85 (1967) 383–429].

Minimal Model Fusion Rules From 2-Groups

AbstractThe fusion rules for the (p,q)-minimal model representations of the Virasoro algebra are shown to come from the group

The 3-state Potts model and Rogers-Ramanujan series

G = \mathbb{Z}_2^{p + q - 5}

Spinor construction of vertex operator algebras, triality, and E[8][(1)]

in the following manner. There is a partition