Moursund Lectures
Cours de Jean-Pierre Serre, no. 16 (1998) , 32 p.
     author = {Serre, Jean-Pierre},
     title = {Moursund {Lectures}},
     series = {Cours de Jean-Pierre Serre},
     number = {16},
     year = {1998},
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TI  - Moursund Lectures
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PY  - 1998
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Serre, Jean-Pierre. Moursund Lectures. Cours de Jean-Pierre Serre, no. 16 (1998), Duckworth, W. E. (red.), 32 p.


These informal notes are closely based on a series of eight lectures given by J.-P. Serre at the University of Oregon in October 1998. Professor Serre gave two talks per week for four weeks.

The first talk each week was concerned with constructing embeddings of finite groups, especially PSL 2 (p) and PGL 2 (p), into Lie groups. The second talk each week was about generalizations of the notion of complete reducibility in group theory, especially in positive characteristic.

The notes are divided into two parts, one for each of the topics of the lecture series. At the end of the notes, there is a short list of references as a guide to further reading.

Table of contents

Part I. Finite subgroups of Lie groups p. 1
Lecture 1p. 2
Lecture 2p. 5
Lecture 3p. 9
Lecture 4p. 12
Part II. The notion of complete reducibility in group theory p. 15
Lecture 1p. 16
Lecture 2p. 20
Lecture 3p. 22
Lecture 4p. 24

[BR] P. Bradley and R. W. Richardson, Étales slices for algebraic transformation groups in characteristic p, Proc. London Math. Soc. 51 (1985), 295-317. | MR | Zbl

[Bo1] A. Borel, Sous-groupes commutatifs et torsion des groupes de Lie compacts connexes, Tôhoku Math. J., (2) 13 (1961), 216-240. | MR | Zbl

[BS] A. Borel and J.-P. Serre, Sur certains sous-groupes des groupes de Lie compacts, Comm. Math. Helv. 27 (1953), 128-133. | MR | Zbl

[BT] A. Borel and J. Tits, Éléments unipotents et sous-groupes paraboliques des groupes réductifs, Invent. Math. 12 (1971), 95-104. | MR | Zbl

[B] N. Bourbaki, Groupes et algèbres de Lie, Chap. I-IV, Hermann, Paris, (1954).

[C] C. Chevalley, Théorie des groupes de Lie, III, Hermann, Paris, (1954). | MR

[D] P. Deligne, Catégories Tannakiennes, The Grothendieck Festschrift, II, Birkhäuser, Boston, (1990), 111-195. | MR | Zbl

[De] M. Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math., 21, (1973), 287-301. | MR | Zbl

[Dy] E. Dynkin, Semisimple subalgebras of semisimple Lie algebra, A. M. S. Translations series 26, (1957), 111-245. | Zbl

[G] R. Griess, Elementary abelian p-subgroups of algebraic groups, Geom. Dedicata 39, (1991), 253-305. | MR | Zbl

[GR] R. Griess and A. Ryba, Finite simple groups which projectively embed in an exceptional Lie Group are classified!, preprint, April 14, (1998). | Zbl | MR

[J1] J. Jantzen, Representations of Algebraic Groups, Academic Press, Orlando, Pure and Applied Mathematics 131, (1987). | MR

[J2] J. Jantzen, Low dimensional representations of reductive groups are semisimple, Algebraic Groups and Lie groups : a volume in honor of R. W. Richardson. Cambridge (1997). | MR | Zbl

[K] B. Kostant, The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group, Amer. J. Math. 81, (1959), 973-1032. | MR | Zbl

[LS] L. Liebeck and G. Seitz, Reductive subgroups of exceptional algebraic groups, Memoirs of the A.M.S. 580 (1996). | MR | Zbl

[Mc] G. Mcninch, Dimensional criteria for semisimplicity of representations, Proc. London Math. Soc. (3) 76 (1998), 95-149. | MR

[Min] H. Minkowski, Gesammelte Abhandlungen, New York, Chelsea Pub. Co. (1967).

[N] M. V. Nori, On subgroups of G L n ( 𝔽 q ) , Invent. Math. 88 (1987), 257-275. | MR | Zbl

[S2] J.-P. Serre, Sur la semi-simplicité des produits tensoriels de représentations de groupes, Invent. Math. 116 (1994), 513-530. | MR | Zbl

[S2] J.-P. Serre, Semisimplicity and tensor products of group representations : converse theorems, J. Algebra 194 (1997), 496-520 (with an appendix by W. Feit). | MR | Zbl

[S3] J.-P. Serre, Exemples de plongements des groupes P S L 2 ( 𝔽 p ) dans des groupes de Lie simples, Invent. Math. 124 (1996), 525-562. | MR | Zbl

[S4] J.-P. Serre, Galois Cohomology, Spriner-Verlag (1997). | MR

[Sp1] T. Springer, Some arithmetical results on semi-simple Lie algebras, Publ. Math. I.H.E.S. 30 (1966), 115-141. | MR | Zbl | Numdam

[Sp2] T. Springer, Regular elements of finite reflection groups, Invent. Math. 25 (1974), 159-198. | MR | Zbl

[SpSt] T. Springer and R. Steinberg, Seminar on algebraic groups and related finite groups : conjugacy classes, algebraic groups, Lect. Notes in Math. 131, Spriner-Verlag (1970). | MR

[St] R. Steinberg, Regular elements of semisimple algebraic groups, Publ. Math. I.H.E.S. 25 (1965), 49-80 (=Coll. Papers no 20). | MR | Numdam

[Te] D. Testerman, The construction of the maximal A 1 ’s in the exceptional algebraic groups. Proc. A.M.S. 161, 635-644 (1993). | MR | Zbl

[T1] J. Tits, Buildings of spherical type and finite BN-pairs, Lect. Notes in Math. 386, Springer-Verlag (1974). | MR | Zbl

[T2] J. Tits, Résumé de cours au Collège de France, (1997-1998), 93-98.