zbMATH — the first resource for mathematics

The arithmetic theory of loop groups. (English) Zbl 0475.17004

17B65 Infinite-dimensional Lie (super)algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
20G05 Representation theory for linear algebraic groups
Full Text: DOI Numdam EuDML
[1] A. Borel,Introduction aux groupes arithmétiques, Paris, Hermann, 1969. · 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. · Zbl 0334.22012
[3] N. Bourbaki,Groupes et algèbres de Lie, chap. 4, 5 et 6, Paris, Hermann, 1968. · Zbl 0186.33001
[4] F. Bruhat etJ. Tits, Groupes réductifs sur un corps local,Publ. Math. I.H.E.S.,41 (1972), 1–251.
[5] F. Bruhat etJ. Tits, Groupes algébriques simples sur un corps local, in theProceedings of a Conference on Local Fields, held at Driebergen (The Netherlands), Edited byT. A. Springer, New York, Springer-Verlag, 1967, pp. 23–36.
[6] H. Garland, Dedekind’s{\(\eta\)}-function and the cohomology of infinite dimensional Lie algebras,Proc. Nat. Acad. Sci. (U.S.A.),72 (1975), 2493–2495. · Zbl 0322.18010
[7] H. Garland, The arithmetic theory of loop algebras,J. Algebra,53 (1978), 480–551. · Zbl 0383.17012
[8] H. Garland andJ. Lepowsky, Lie algebra homology and the Macdonald-Kac formulas,Inventiones math.,34 (1976), 37–76. · Zbl 0358.17015
[9] N. Iwahori andH. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings ofp-adic Chevalley groups,Publ. Math. I.H.E.S.,25 (1965), 237–280. · Zbl 0228.20015
[10] V. G. Kac, Simple irreducible 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.
[11] V. G. Kac, Infinite-dimensional Lie algebras and Dedekind’s{\(\eta\)}-function (in Russian),Funkt. Anal. i Ego Prilozheniya,8 (1974), 77–78; English translation:Functional Analysis and its Applications,8 (1974), 68–70. · Zbl 0298.57019
[12] R. Marcuson, Tits systems in generalized nonadjoint Chevalley groups,J. Algebra,34 (1975), 84–96. · 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. · Zbl 0261.20025
[14] J. Milnor,Introduction to algebraic K-theory, Princeton, Princeton University Press, 1971. · Zbl 0237.18005
[15] R. V. Moody, A new class of Lie algebras,J. Algebra,10 (1968), 211–230. · Zbl 0191.03005
[16] R. V. Moody, Euclidean Lie algebras,Can. J. Math.,21 (1969), 1432–1454. · Zbl 0194.34402
[17] R. V. Moody andK. L. Teo, Tits’ systems with crystallographic Weyl groups,J. Algebra,21 (1972), 178–190. · Zbl 0232.20089
[18] C. C. Moore, Group extensions ofp-adic and adelic linear groups,Publ. Math. I.H.E.S.,35 (1968), 157–222.
[19] J.-P. Serre,Algèbres de Lie semi-simples complexes, New York, Benjamin, 1966. · 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.
[21] R. Steinberg,Lectures on Chevalley groups, Yale University mimeographed notes, 1967. · Zbl 0164.34302
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.