A character approach to Looijenga's invariant theory for generalized root systems
Compositio Mathematica, Tome 55 (1985) no. 1, pp. 3-32. 
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     title = {A character approach to {Looijenga's} invariant theory for generalized root systems},
     journal = {Compositio Mathematica},
     pages = {3--32},
     publisher = {Martinus Nijhoff Publishers},
     volume = {55},
     number = {1},
     year = {1985},
     mrnumber = {791645},
     zbl = {0609.20024},
     language = {en},
     url = {http://www.numdam.org/item/CM_1985__55_1_3_0/}
}
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Slodowy, Peter. A character approach to Looijenga's invariant theory for generalized root systems. Compositio Mathematica, Tome 55 (1985) no. 1, pp. 3-32. http://www.numdam.org/item/CM_1985__55_1_3_0/

[1] N. Bourbaki: Groupes et algèbres de Lie, IV, V, VI, Hermann, Paris (1968). | MR

[2] E. Brieskorn: Singular elements of semisimple algebraic groups, Actes Congrès Intern, Math. (1970) t. 2, 279-284. | MR | Zbl

[3] I. Frenkel and V. Kac: Basic representations of affine Lie algebras and dual resonance models, Inventiones Math. 62 (1980) 23-66. | MR | Zbl

[4] O. Gabber and V. Kac: On defining relations of certain infinite-dimensional Lie algebras, Bull. AMS, New Ser, 5 (1981) 185-189. | MR | Zbl

[5] H. Garland and J. Lepowsky: Lie algebra homology and the Macdonald-Kac formulas, Inventiones Math. 34 (1976) 37-76. | MR | Zbl

[6] H. Garland: The arithmetic theory of loop algebras, J. Algebra 53 (1978) 480-551. | MR | Zbl

[7] H. Garland: The arithmetic theory of loop groups, Publ. Math. I.H.E.S. 52 (1980) 5-136. | Numdam | MR | Zbl

[8] V. Kac: Simple irreducible graded Lie algebras of finite growth, Math. USSR Izvestija 2 (1968) 1271-1311. | MR | Zbl

[9] V. Kac: An algebraic definition of the compact Lie groups, Trudy MIEM 5 (1969) 36-47 (in Russian).

[10] V. Kac: Infinite-dimensional Lie algebras and Dedekind's η-function, Functional Anal. Appl. 8 (1974) 68-70. | Zbl

[11] V. Kac: Infinite-dimensional algebras, Dedekind's η-function, classical Möbius function and the very strange formula, Advances in Math. 30 (1978) 85-136. | Zbl

[12] V. Kac: Infinite root systems, representations of graphs, and invariant theory, Inventiones Math. 56 (1980) 57-92. | MR | Zbl

[13] V. Kac and D. Peterson: Affine Lie algebras and Hecke modular forms, Bull. AMS 3 (1980) 1057-1061. | MR | Zbl

[14] V. Kac and D. Peterson: Infinite-dimensional Lie algebras, θ-functions, and modular forms. Advances in Math. 53 (1984) 125-264. | Zbl

[15] J. Lepowsky and R.V. Moody: Hyperbolic Lie algebras and quasiregular cusps on Hilbert modular surfaces, Math. Ann. 245 (1979) 63-88. | MR | Zbl

[16] E. Looijenga: Root systems and elliptic curves, Inventiones Math. 38 (1976) 17-32. | MR | Zbl

[17] E Looijenga:On the semi-universal deformation of a simple elliptic singularity II, Topology 17 (1978) 23-40. | MR | Zbl

[18] E. Looijenga: Invariant theory for generalized root systems, Inventiones Math. 61 (1980) 1-32. | MR | Zbl

[19] E. Looijenga: Rational surfaces with an anti-canonical cycle, Annals of Math. 114 (1981) 267-322. | MR | Zbl

[20] I.G. Macdonald ! Affine root systems and Dedekind's η-function, Inventiones Math. 15 (1972) 91-143. | Zbl

[21] R. Marcuson: Tits' systems in generalized nonadjoint Chevalley groups, J. Algebra 34 (1975) 84-96. | MR | Zbl

[22] J.Y. Merindol: Déformations des surfaces de del Pezzo, de points doubles rationnels et des cônes sur une courbe elliptique, Thèse 3eme cycle, Université de Paris VII, 1980.

[23] A. Meurman: Characters of rank two hyperbolic Lie algebras as functions at quasiregular cusps. J. Algebra 76 (1982) 494-504. | MR | Zbl

[24] R.V. Moody: A new class of Lie algebras, J. Algebra 10 (1968) 211-230. | MR | Zbl

[25] R.V. Moody: Euclidean Lie algebras, Can. J. Math. 21 (1969) 1434-1454. | MR | Zbl

[26] R.V. Moody, K.L. Teo: Tits' systems with cristallographic Weyl groups, J. Algebra 21 (1972) 178-190. | MR | Zbl

[27] H. Pinkham: Simple elliptic singularities, Del Pezzo surfaces and Cremona transformations, Proc. Symp. Pure Math. 30 (1977) 69-71. | MR | Zbl

[28] P. Slodowy: Simple singularities and simple algebraic groups, Lecture Notes In Math. 815, Springer, Berlin-Heidelberg -New York (1980). | MR | Zbl

[29] P. Slodowy: Chevalley groups over C((t)) and deformations of simply elliptic singularities, RIMS Kokyuroku 415, 19-38, Kyoto University (1981). | MR

[30] P. Slodowy: Adjoint quotients for Kac-Moody groups and deformations of special singularities, Seminar talks, Paris, March 1981.

[31] P. Steinberg: Regular elements of semisimple algebraic groups, Publ. Math. I. H. E. S. 25 (1965) 49-80. | Numdam | MR | Zbl

[32] R. Steinberg: Conjugacy classes in algebraic groups, Lecture Notes in Math. 366, Springer, Berlin-Heidelberg -New York (1974). | MR | Zbl

[33] J. Tits: Resumé de cours, Annuaire du Collège de France 1980-1981, 1981-1982, Collège de France, Paris.

[34] J. Tits: Définition par générateurs et relations de groupes avec BN-paires, C.R. Acad. Sc. Paris 293 (1981) 317-322. | MR | Zbl

[35] E. Vinberg: Discrete linear groups generated by reflections, Math. USSR Izvestija 35 (1971) 1083-1119. | MR | Zbl

[36] V.G. Kac and D.H. Peterson: Unitary structure in representations of infinite-dimensional groups and a convexity theorem, Inventiones Math. 76 (1984) 1-14. | MR | Zbl