@incollection{SB_1988-1989__31__7_0, author = {Tits, Jacques}, title = {Groupes associ\'es aux alg\`ebres de {Kac-Moody}}, booktitle = {S\'eminaire Bourbaki : volume 1988/89, expos\'es 700-714}, series = {Ast\'erisque}, note = {talk:700}, pages = {7--31}, publisher = {Soci\'et\'e math\'ematique de France}, number = {177-178}, year = {1989}, mrnumber = {1040566}, zbl = {0705.17018}, language = {fr}, url = {http://archive.numdam.org/item/SB_1988-1989__31__7_0/} }
TY - CHAP AU - Tits, Jacques TI - Groupes associés aux algèbres de Kac-Moody BT - Séminaire Bourbaki : volume 1988/89, exposés 700-714 AU - Collectif T3 - Astérisque N1 - talk:700 PY - 1989 SP - 7 EP - 31 IS - 177-178 PB - Société mathématique de France UR - http://archive.numdam.org/item/SB_1988-1989__31__7_0/ LA - fr ID - SB_1988-1989__31__7_0 ER -
%0 Book Section %A Tits, Jacques %T Groupes associés aux algèbres de Kac-Moody %B Séminaire Bourbaki : volume 1988/89, exposés 700-714 %A Collectif %S Astérisque %Z talk:700 %D 1989 %P 7-31 %N 177-178 %I Société mathématique de France %U http://archive.numdam.org/item/SB_1988-1989__31__7_0/ %G fr %F SB_1988-1989__31__7_0
Tits, Jacques. Groupes associés aux algèbres de Kac-Moody, dans Séminaire Bourbaki : volume 1988/89, exposés 700-714, Astérisque, no. 177-178 (1989), Exposé no. 700, 25 p. http://archive.numdam.org/item/SB_1988-1989__31__7_0/
[AT] Groups associated with some types of infinite dimensional Lie algebras, preprint, University of Tsukuba, 1988 (revised 1989) . | MR
and -[BaPV] Compact complex surfaces, Ergebnisse d. Math. 3. Folge, Bd. 4, Springer-Verlag, 1984. | MR | Zbl
, , -[Bau] Étude et classification des automorphismes d'ordre fini et de première espèce des algèbres de Kac-Moody affines, thèse, Université de Nancy I, septembre 1985. | MR | Zbl
-[BauR] Algèbres de Kac-Moody affines (automorphismes et formes réelles), Publications de l'Institut Elie Cartan, n° 11, 1989. | MR | Zbl
et -[Bo] Groupes et algèbres de Lie, Chap. IV, V, VI, Actu. Sci. et Ind. n° 1337, Hermann, Paris, 1968. | MR | Zbl
-[BrT 1] Groupes algébriques simples sur un corps local, Proc. Conf. local fields (Driebergen, 1966), Springer-Verlag, 1967, 23-36. | MR | Zbl
ET -[BrT 2] Groupes réductifs sur un corps local, II, Publ. Math. I.H.E.S. 60 (1984), 5-184. | Numdam | MR | Zbl
et -[Ch 1] Séminaire sur la classification des groupes de Lie algébriques 1956-1958, 2 vol. multigraphiés, Inst. H. Poincaré, Paris, 1958. | Zbl
-[Ch 2] Certains schémas de groupes semi-simples, Sém. Bourbaki, exposé n° 219, mai 1961, Benjamin, New York, 1966. | Numdam | MR | Zbl
-[De] Schémas en groupes réductifs, Bull. Soc. Math. Fr. 93 (1965), 369-413. | Numdam | MR | Zbl
-[Di] Algèbres enveloppantes, Gauthier-Villars, Paris, 1974. | MR | Zbl
-[Ga 1] The arithmetic theory of loop algebras, J. Algebra, 53 (1978), 480-551. | MR | Zbl
-[Ga 2] The arithmetic theory of loop groups, Publ. Math. I.H.E.S. 52 (1980), 5-136. | Numdam | MR | Zbl
-[GoW] Structure and unitary cocycle representations of loop groups and the group of diffeomorphisms of the circle, Jour. r. angew. Math. 347 (1984), 69-133. | MR | Zbl
and -[GuS] Cohomologie des variétés de drapeaux infinies, C.R. Acad. Sci. Paris, 296 (1983), Sér. I, 425-427. | MR | Zbl
et -[Hi] On the arithmetic of p-adic Steinberg groups, preprint, Yale University, 1964.
-[IDGA] Infinite dimensional groups with applications, V. Kac ed., MSRI publications n° 4, Springer-Verlag, 1985. | MR | Zbl
[IM] On some Bruhat decomposition and the structure of the Hecke ring of p-adic Chevalley groups, Publ. Math. I.H.E.S. 25 (1965), 5-48. | Numdam | MR | Zbl
and -[Kac 1] Simple irreducible graded Lie algebras of finite growth, Izvestija Akad. Nauk. S.S.S.R. (Ser. mat.) 32 (1968), 1923-1967 ; Math. U.S.S.R. Izvestija 2 (1968), 1271-1311. | MR | Zbl
-[Kac 2] Infinite dimensional Lie algebras, Progr. Math. n° 44, Birkhäuser, Boston, 1983 ; 2nd edition, Cambridge Univ. Press, Cambridge, 1985. | MR | Zbl
-[Kac 3] Constructing groups associated to infinite-dimensional Lie algebras, in [IDGA], 167-216. | MR | Zbl
-[KacP 1] Regular functions on some infinite-dimensional groups, in Arithmetic and Geometry, M. Artin and J. Tate ed., Birkhäuser, Boston, 1983, 141-166. | MR | Zbl
and -[KacP 2] Unitary structure in representations of infinite-dimensional groups and a convexity theorem, Inventiones Math. 76 (1984), 1-14. | MR | Zbl
and -[KacP 3] Defining relations of certain infinite dimensional groups, in Élie Cartan et les Mathématiques d'aujourd'hui, Astérisque, n° hors série, 1985, 165-208. | Numdam | MR | Zbl
and -[KacP 4] On geometric invariant theory for infinite dimensional groups, in Algebraic groups, Utrecht 1986, A. Cohen, W. Hesselink, W. van der Kallen, J. Strooker ed., Springer Lecture Notes 1271 (1987), 109-142. | MR | Zbl
and -[Kan 1] Infinite dimensional simple graded Lie algebras, Dokl. Akad. Nauk. S.S.S.R. 179 (1968), 534-537 ; Sov. Math. Dokl. 9 (1968), 409-412. | MR | Zbl
-[Kan 2] Graded Lie algebras, Trudy sem. Vect. Tens. Anal. 15 (1970), 227-266. | MR | Zbl
-[KL 1] Representations of Coxeter groups and Hecke algebras, Inv. Math. 53 (1979), 165-184. | MR | Zbl
and -[KL 2] Schubert varieties and Poincaré duality, Proc. Symp. Pure Math. A.M.S. 36 (1980), 185-203. | MR | Zbl
and -[Ko] Groups over Z , in Algebraic groups and discontinuous subgroups (Boulder, 1965), Proc. Symp. Pure Math. 9, A.M.S. 1966, 90-98. | MR | Zbl
-[KoK] The nil Hecke ring and cohomology of G/P for a Kac-Moody group G , Proc. Nat. Acad. Sci. U.S.A. 83 (1986), 1543-1545. | MR | Zbl
and -[Ku 1] Cohomology algebra of Schubert varieties associated to Kac-Moody groups, Proc. Conf. Algebraic Geom., Vancouver, 1984, C.M.S. Conf. Proc. 6 (1986), 277-299. | MR | Zbl
-[Ku 2] Demazure character formula in arbitrary Kac - Moody setting, Inventiones Math. 89 (1987), 395-423. | MR | Zbl
-[Ku 3] Proof of the Partarasarathy - Ranga Rao - Varadarajan conjecture, Preprint, 1987. | MR
-[Le] Generalized Verma modules, loop space cohomology and Macdonald type identities, Ann. Sci. Ec. Norm. Sup. 12 (1979), 169-234. | Numdam | MR | Zbl
-[Mar] Tits' systems in generalized nonadjoint Chevalley groups, J. of Algebra 34 (1975) , 84-96. | MR | Zbl
-[Mat 1] Sur la construction de groupes associés aux algèbres de Kac-Moody, C.R. Acad. Sci. Paris 299 (1984), Sér. I, 161-164. | MR | Zbl
-[Mat 2] Formules de Demazure - Weyl et généralisation du théorème de Borel - Weil - Bott, C.R. Acad. Sci. Paris 303 (1986), Sér. I, 391- 394. | MR | Zbl
-[Mat 3] Fibrés en droites sur les variétés de Schubert associées aux algèbres de Kac-Moody, Proc. Symp. on topological methods in field theory, Helsinki, 1986, Scientific World 1987, 111-115. | MR | Zbl
-[Mat 4] Classes canoniques des variétés de Schubert et algèbres affines, C.R. Acad. Sci. Paris 305 (1987), Sér. I, 105-107. | MR | Zbl
-[Mat 5] Construction du groupe de Kac-Moody et applications, C.R. Acad. Sci. Paris, Sér. I, 306 (1988), 227-230. | MR | Zbl
-[Mat 6] Formules de Weyl et de Demazure et théorème de Borel-Weil-Bott pour les algèbres de Kac-Moody générales, I, II, prépublications, 1986, 1988. Formules de caractères pour les algèbres de Kac-Moody générales, Astérisque n° 159-160, 1988. | Numdam | MR
-[Mat 7] Construction d'un groupe de Kac-Moody et applications, Compositio Math. 69 (1989), 37-60. | Numdam | MR | Zbl
-[Mi] Integral bases for affine Lie algebras and their applications, Contemporary Math. 40, Amer. Math. Soc. , 1985. | MR | Zbl
-[Moo 1] A new class of Lie algebras, J. Algebra 10 (1968), 211-230. | MR | Zbl
-[Moo 2] A simplicity theorem for Chevalley groups defined by generalized Cartan matrices, preprint, april 1982.
-[MooT] Tits' systems with crystallographic Weyl groups, J. Algebra 21 (1972), 178-190. | MR | Zbl
and -[Mor 1] On adjoint Chevalley groups associated with completed Euclidean Lie algebras, Comm. in Algebra 12 (1984), 673-690. | MR | Zbl
-[Mor 2] Coverings, generators and relations of certain infinite-dimensional groups, preprint, 1983.
-[Mor 3] Conjugate classes of three dimensional simple Lie subalgebras of the affine Lie algebra Al(1) , in Algebraic and topological theories (to the memory of T. Miyata), 1985, 113-126. | MR | Zbl
-[Mor 4] Commutator relations in Kac - Moody groups, Proc. Japan Acad. 63 (1987), sér. A, 21-22. | MR | Zbl
-[PK] Infinite flag varieties and conjugacy theorems, Proc. Nat. Acad. Sci. U.S.A. 80 (1983), 1778-1782. | MR | Zbl
and -[PS] Loop groups, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1986. | MR | Zbl
and -[ReS] Reduction of Hamiltonian systems, affine Lie algebras and Lax equations, I, Invent. Math. 54 (1979), 81-100 ; II, ibid. 63 (1981), 423-432. | MR | Zbl
and - -[Ro] Formes réelles presque compactes des algèbres affines, prépublication, Nancy, 1988.
-[Seg 1] Unitary representations of some infinite dimensional groups, Comm. Math. Phys. 80 (1981), 301-342. | MR | Zbl
-[Seg 2] Loop groups, in Arbeitstagung, Bonn 1984, Lecture Notes in Math. Nr. 1111, Springer-Verlag 1985, 155-168. | MR | Zbl
-[SegW] Loop groups and equations of KdV type, Publ. Math. I.H.E.S. 61 (1985), 5-65. | Numdam | MR | Zbl
and -[Ser 1] Algèbres de Lie semi-simples complexes, W.A. Benjamin, New York, 1966. | MR | Zbl
-[Ser 2] Arbres, amalgames, Sl2 , Astérisque n° 46, Soc. Math. Fr., 1977. | Numdam | MR | Zbl
-[Sl 1] Singularitäten, Kac-Moody Liealgebren, assoziierte Gruppen und Verallgemeinerungen, Habilitationsschrift, Bonn, 1984.
-[Sl 2] An adjoint quotient for certain groups attached to Kac-Moody algebras, in [IDGA], 307-333. | MR | Zbl
-[Su 1] Groups associated with compact type subalgebras of Kac-Moody algebras, Proc. Japan Acad. 62 A (1986), 392-395. | MR | Zbl
-[Su 2] Groups associated with unitary forms of Kac-Moody algebras, J. Math. Soc. Japan 40 (1988), 85-104. | MR | Zbl
-[Su 3] Exponentials of certain completions of the unitary form of a Kac-Moody algebra, Proc. Japan Acad. 64 A (1988), 208-211. | MR | Zbl
-[Ti 1] Résumé de cours, Annuaire du Collège de France, 81e année (1980-1981), 75-86.
-[Ti 2] Résumé de cours, Annuaire du Collège de France, 82e année (1981-1982), 91-105.
-[Ti 3] Groups and group functors attached to Kac-Moody data, in Arbeitstagung, Bonn 1984, Springer Lecture Notes Nr. 1111, 1985, 193-223. | MR | Zbl
-[Ti 4] Buildings and group amalgamations, in Groups, St. Andrews 1985, Lecture Notes Series n° 121, Lond. Math. Soc., 1986, 110-127. | MR | Zbl
-[Ti 5] Ensembles ordonnés, immeubles et sommes amalgamées, Bull. Soc. Math. (Sér. A) 38 (1986) , 367-387. | MR | Zbl
-[Ti 6] Uniqueness and presentation of Kac-Moody groups over fields, J. of Algebra, 105 (1987), 542-573. | MR | Zbl
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