Geodesic
Folded fans and string functions
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 197-212 
M. Ilyin; P. Kulish; V. Lyakhovsky. Folded fans and string functions. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 21, Tome 374 (2010), pp. 197-212. http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a10/
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     author = {M. Ilyin and P. Kulish and V. Lyakhovsky},
     title = {Folded fans and string functions},
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     year = {2010},
     volume = {374},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2010_374_a10/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The folded fans $F\Psi$ describe the recursion properties for the weights of integrable highest weight modules $L^\mu$. Being considered simultaneously for the set of string functions $\sigma_s^\mu$ belonging to the fundamental Weyl chamber and corresponding to the same congruence class the system of recursion relations gives rise to an equation that connect the string functions and the power series depending on the multiplicities of the folded fan $F\Psi$ weights. We apply these equations to study the properties of string functions $\sigma_s^\mu$ associated to the integrable modules for affine Lie algebras. New important relations for string functions are thus obtained. The set of folded fans provides a compact and effective tool to study them. Bibl. – 7 titles.

[1] W. Fulton, J. Harris, Representation theory, A first course, Graduate text in Math., 129, Springer, NY, 1991 | MR | Zbl

[2] V. Kac, Infinite Dimensional Lie Algebras, 3rd edition, Cambridge Univ. Press, 1990 | MR | Zbl

[3] M. Wakimoto, Infinite-Dimensional Lie Algebras, Translations of Mathematical Monographs, 195, Amer. Math. Soc., 2001 | MR | Zbl

[4] M. Wakimoto, Lectures on Infinite-Dimensional Lie Algebra, World Scientific, 2005 | MR | Zbl

[5] V. D. Lyakhovsky, S. Yu. Melnikov, “Recursion relations and branching rules for simple Lie algebras”, J. Phys. A, 29 (1996), 1075–1087 | DOI | MR | Zbl

[6] M. Ilyin, P. Kulish, V. Lyakhovsky, “On a property of branching coefficients for affine Lie algebras”, Algebra Analiz, 21:2 (2009), 52–70 ; arXiv: 0812.2124 | MR

[7] P. Kulish, V. Lyakhovsky, “String functions for affine Lie algebras integrable modules”, SIGMA, 4 (2008), 085 ; arXiv: 0812.2381 | MR | Zbl