A new perspective on the Frenkel-Zhu fusion rule theorem

JOURNAL OF ALGEBRA

卷:320

Article

Feingold, Alex J.¹  Fredenhagen, Stefan² 

[1] SUNY Binghamton, Dept Math Sci, Binghamton, NY 13902 USA

[2] Albert Einstein Inst, Max Planck Inst Gravitationphys, D-14476 Golm, Germany

关键词: fusion rules;    affine Kac-Moody algebras;   

DOI  :  10.1016/j.jalgebra.2008.05.026

来源: Elsevier

【 摘 要 】

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]. (C) 2008 Elsevier Inc. All rights reserved.

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