The arithmetic theory of loop groups
Garland, Howard
Publications Mathématiques de l'IHÉS, Tome 52 (1980), p. 5-136 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{PMIHES_1980__52__5_0,
     author = {Garland, Howard},
     title = {The arithmetic theory of loop groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     volume = {52},
     year = {1980},
     pages = {5-136},
     mrnumber = {83a:20057},
     zbl = {0475.17004},
     language = {en},
     url = {http://dml.mathdoc.fr/item/PMIHES_1980__52__5_0}
}

Garland, Howard. The arithmetic theory of loop groups. Publications Mathématiques de l'IHÉS, Tome 52 (1980) pp. 5-136. http://gdmltest.u-ga.fr/item/PMIHES_1980__52__5_0/

[1] A. Borel, Introduction aux groupes arithmétiques, Paris, Hermann, 1969. | MR 39 #5577 | Zbl 0186.33202

[2] A. Borel, Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup, Inventiones math., 35 (1976), 233-259. | MR 56 #3196 | Zbl 0334.22012

[3] N. Bourbaki, Groupes et algèbres de Lie, chap. 4, 5 et 6, Paris, Hermann, 1968.

[4] F. Bruhat et J. Tits, Groupes réductifs sur un corps local, Publ. Math. I.H.E.S., 41 (1972), 1-251. | Numdam | MR 48 #6265 | Zbl 0254.14017

[5] F. Bruhat et J. Tits, Groupes algébriques simples sur un corps local, in the Proceedings of a Conference on Local Fields, held at Driebergen (The Netherlands), Edited by T. A. SPRINGER, New York, Springer-Verlag, 1967, pp. 23-36. | MR 37 #6396 | Zbl 0263.14016

[6] H. Garland, Dedekind's η-function and the cohomology of infinite dimensional Lie algebras, Proc. Nat. Acad. Sci. (U.S.A.), 72 (1975), 2493-2495. | MR 52 #8204 | Zbl 0322.18010

[7] H. Garland, The arithmetic theory of loop algebras, J. Algebra, 53 (1978), 480-551. | MR 80a:17012 | Zbl 0383.17012

[8] H. Garland and J. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas, Inventions math., 34 (1976), 37-76. | MR 54 #2744 | Zbl 0358.17015

[9] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. I.H.E.S., 25 (1965), 237-280. | Numdam | MR 32 #2486 | Zbl 0228.20015

[10] V. G. Kac, Simple irreductible graded Lie algebras of finite growth (in Russian), Izv. Akad. Nauk. SSSR, 32 (1968), 1323-1367 ; English translation : Math. USSR-Izvestija, 2 (1968), 1271-1311. | Zbl 0222.17007

[11] V. G. Kac, Infinite-dimensional Lie algebras and Dedekind's η-function (in Russian), Funkt. Anal. i Ego Prilozheniya, 8 (1974), 77-78 ; English translation : Functional Analysis and its Applications, 8 (1974), 68-70. | MR 51 #10410 | Zbl 0299.17005

[12] R. Marcuson, Tits systems in generalized nonadjoint Chevalley groups, J. Algebra, 34 (1975), 84-96. | MR 53 #3146 | Zbl 0338.20054

[13] H. Matsumoto, Sur les sous-groupes arithmétiques des groupes semi-simples déployés, Ann. Scient. Éc. Norm. Sup., 2 (4th series) (1969), 1-62. | Numdam | MR 39 #1566 | Zbl 0261.20025

[14] J. Milnor, Introduction to algebraic K-theory, Princeton, Princeton University Press, 1971. | MR 50 #2304 | Zbl 0237.18005

[15] R. V. Moody, A new class of Lie algebras, J. Algebra, 10 (1968), 211-230. | MR 37 #5261 | Zbl 0191.03005

[16] R. V. Moody, Euclidean Lie algebras, Can. J. Math., 21 (1969), 1432-1454. | MR 41 #287 | Zbl 0194.34402

[17] R. V. Moody and K. L. Teo, Tits' systems with crystallographic Weyl groups, J. Algebra, 21 (1972), 178-190. | MR 47 #8705 | Zbl 0232.20089

[18] C. C. Moore, Group extensions of p-adic and adelic linear groups, Publ. Math. I.H.E.S., 35 (1968), 157-222. | Numdam | MR 39 #5575 | Zbl 0159.03203

[19] J.-P. Serre, Algèbres de Lie semi-simples complexes, New York, Benjamin, 1966. | MR 35 #6721 | Zbl 0144.02105

[20] R. Steinberg, Générateurs, relations et revêtements de groupes algébriques, in Colloque sur la Théorie des Groupes algébriques, held in Brussels, 1962, Paris, Gauthier-Villars, 1962, pp. 113-127. | MR 27 #3638 | Zbl 0272.20036

[21] R. Steinberg, Lectures on Chevalley groups, Yale University mimeographed notes, 1967.