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The arithmetic theory of loop groups
Publications Mathématiques de l'IHÉS, Volume 52 (1980), pp. 5-136
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DOI: 10.1007/BF02684779 
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     author = {Howard Garland},
     title = {The arithmetic theory of loop groups},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     pages = {5--136},
     year = {1980},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {52},
     doi = {10.1007/BF02684779},
     mrnumber = {83a:20057},
     zbl = {0475.17004},
     language = {en},
     url = {https://pmihes.centre-mersenne.org/articles/10.1007/BF02684779/}
}
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Howard Garland. The arithmetic theory of loop groups. Publications Mathématiques de l'IHÉS, Volume 52 (1980), pp. 5-136. doi: 10.1007/BF02684779

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

[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. | Zbl | MR

[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. | Zbl | MR | Numdam

[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. | Zbl | MR

[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. | Zbl | MR

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

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

[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. | Zbl | MR | Numdam

[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

[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. | Zbl | MR

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

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

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

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

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

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

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

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

[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. | Zbl | MR

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

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