A character approach to Looijenga's invariant theory for generalized root systems
Slodowy, Peter
Compositio Mathematica, Tome 56 (1985), p. 3-32 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1985-01-01
@article{CM_1985__55_1_3_0,
     author = {Slodowy, Peter},
     title = {A character approach to Looijenga's invariant theory for generalized root systems},
     journal = {Compositio Mathematica},
     volume = {56},
     year = {1985},
     pages = {3-32},
     mrnumber = {791645},
     zbl = {0609.20024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1985__55_1_3_0}
}

Slodowy, Peter. A character approach to Looijenga's invariant theory for generalized root systems. Compositio Mathematica, Tome 56 (1985) pp. 3-32. http://gdmltest.u-ga.fr/item/CM_1985__55_1_3_0/

[1] N. Bourbaki: Groupes et algèbres de Lie, IV, V, VI, Hermann, Paris (1968). | MR 240238

[2] E. Brieskorn: Singular elements of semisimple algebraic groups, Actes Congrès Intern, Math. (1970) t. 2, 279-284. | MR 437798 | Zbl 0223.22012

[3] I. Frenkel and V. Kac: Basic representations of affine Lie algebras and dual resonance models, Inventiones Math. 62 (1980) 23-66. | MR 595581 | Zbl 0493.17010

[4] O. Gabber and V. Kac: On defining relations of certain infinite-dimensional Lie algebras, Bull. AMS, New Ser, 5 (1981) 185-189. | MR 621889 | Zbl 0474.17007

[5] H. Garland and J. Lepowsky: Lie algebra homology and the Macdonald-Kac formulas, Inventiones Math. 34 (1976) 37-76. | MR 414645 | Zbl 0358.17015

[6] H. Garland: The arithmetic theory of loop algebras, J. Algebra 53 (1978) 480-551. | MR 502647 | Zbl 0383.17012

[7] H. Garland: The arithmetic theory of loop groups, Publ. Math. I.H.E.S. 52 (1980) 5-136. | Numdam | MR 601519 | Zbl 0475.17004

[8] V. Kac: Simple irreducible graded Lie algebras of finite growth, Math. USSR Izvestija 2 (1968) 1271-1311. | MR 259961 | Zbl 0222.17007

[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 0299.17005

[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 0391.17010

[12] V. Kac: Infinite root systems, representations of graphs, and invariant theory, Inventiones Math. 56 (1980) 57-92. | MR 557581 | Zbl 0427.17001

[13] V. Kac and D. Peterson: Affine Lie algebras and Hecke modular forms, Bull. AMS 3 (1980) 1057-1061. | MR 585190 | Zbl 0457.17007

[14] V. Kac and D. Peterson: Infinite-dimensional Lie algebras, θ-functions, and modular forms. Advances in Math. 53 (1984) 125-264. | Zbl 0584.17007

[15] J. Lepowsky and R.V. Moody: Hyperbolic Lie algebras and quasiregular cusps on Hilbert modular surfaces, Math. Ann. 245 (1979) 63-88. | MR 552580 | Zbl 0396.17007

[16] E. Looijenga: Root systems and elliptic curves, Inventiones Math. 38 (1976) 17-32. | MR 466134 | Zbl 0358.17016

[17] E Looijenga:On the semi-universal deformation of a simple elliptic singularity II, Topology 17 (1978) 23-40. | MR 492380 | Zbl 0392.57013

[18] E. Looijenga: Invariant theory for generalized root systems, Inventiones Math. 61 (1980) 1-32. | MR 587331 | Zbl 0436.17005

[19] E. Looijenga: Rational surfaces with an anti-canonical cycle, Annals of Math. 114 (1981) 267-322. | MR 632841 | Zbl 0509.14035

[20] I.G. Macdonald ! Affine root systems and Dedekind's η-function, Inventiones Math. 15 (1972) 91-143. | Zbl 0244.17005

[21] R. Marcuson: Tits' systems in generalized nonadjoint Chevalley groups, J. Algebra 34 (1975) 84-96. | MR 399295 | Zbl 0338.20054

[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 661868 | Zbl 0481.17004

[24] R.V. Moody: A new class of Lie algebras, J. Algebra 10 (1968) 211-230. | MR 229687 | Zbl 0191.03005

[25] R.V. Moody: Euclidean Lie algebras, Can. J. Math. 21 (1969) 1434-1454. | MR 255627 | Zbl 0194.34402

[26] R.V. Moody, K.L. Teo: Tits' systems with cristallographic Weyl groups, J. Algebra 21 (1972) 178-190. | MR 320165 | Zbl 0232.20089

[27] H. Pinkham: Simple elliptic singularities, Del Pezzo surfaces and Cremona transformations, Proc. Symp. Pure Math. 30 (1977) 69-71. | MR 441969 | Zbl 0391.14006

[28] P. Slodowy: Simple singularities and simple algebraic groups, Lecture Notes In Math. 815, Springer, Berlin-Heidelberg -New York (1980). | MR 584445 | Zbl 0441.14002

[29] P. Slodowy: Chevalley groups over C((t)) and deformations of simply elliptic singularities, RIMS Kokyuroku 415, 19-38, Kyoto University (1981). | MR 708340

[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 180554 | Zbl 0136.30002

[32] R. Steinberg: Conjugacy classes in algebraic groups, Lecture Notes in Math. 366, Springer, Berlin-Heidelberg -New York (1974). | MR 352279 | Zbl 0281.20037

[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 637803 | Zbl 0548.20019

[35] E. Vinberg: Discrete linear groups generated by reflections, Math. USSR Izvestija 35 (1971) 1083-1119. | MR 302779 | Zbl 0256.20067

[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 739620 | Zbl 0534.17008