Homogeneous spaces

Some references

Michael Atiyah et al., Representation theory of Lie groups, LMS Lecture Note Series 34
Michael Atiyah and Raoul Bott: The moment map and equivariant cohomology, Topology 23:1
I.N. Bernstein, I.M. Gelfand, and S.I. Gelfand: Schubert cells and the cohomology of the spaces G/P, Uspehi Mat. Nauk 28 (no. 3): 3 (in Russian); Russian Math. Surveys 28:1 (in English); English translation reprinted in Representation Theory, LMS Lecture Note Series 69.
Andrzej Bialynicki-Birula: Some theorems on actions of algebraic groups, Annals of Math 98:480
Armand Borel: Linear algebraic groups
Armand Borel: Lecture Notes in Math. 36
Armand Borel: Kahlerian coset spaces of simple groups, Proc. Nat. Acad. Sci. 40:1147
Nicolas Bourbaki: Groupes et algebres de Lie, chapter 5.
Raoul Bott: Homogeneous vector bundles, Annals of Math 66:203
Raoul Bott and Loring Tu: Differential forms in algebraic topology
Theodor Bröcker and Tammo tom Dieck: Representations of compact Lie groups
William M. Boothby: Intro to differentiable manifolds and homogeneous spaces
Roger Carter, Graeme Segal, and Ian Macdonald, Lectures on Lie groups and Lie algebras, LMS Student Texts 32. Highly recommended
Claude Chevalley: Theory of Lie groups
Michel Demazure: A very simple proof of Bott's theorem, Inventiones 33:271
A.T. Fomenko, D.B. Fuchs, and V.L. Gutenmacher: Homotopic topology
Victor Guillemin and Shlomo Sternberg: Supersymmetry and equivariant de Rham theory
Allen Hatcher: Algebraic topology; also, Spectral sequences in algebraic topology, unpublished manuscript; both available from www.math.cornell.edu/~hatcher
Sigurdur Helgason: Groups and geometric analysis : integral geometry, invariant differential operators, and spherical functions
James Humphreys: Reflection groups and Coxeter groups
Gerhard Hochschild: The structure of Lie groups
Dale Husemoller: Fibre bundles
Shrawan Kumar, Kac-Moody groups, their flag varieties and representation theory
Saunders Mac Lane, Homology
John Milnor: Construction of universal bundles II, Ann. of Math. 63:430.
John Milnor and James Stasheff: Characteristic classes
David Mumford, John Fogarty and Frances Kirwan: Geometric invariant theory
Edwin Spanier, Algebraic topology
James Stasheff, A classification theorem for fibre spaces, Topology 2:239.
Norman Steenrod: The topology of fibre bundles

Lecture 1 (4 Sept) Steenrod I, Husemoller I (fiber bundles), Boothby IV (homogeneous spaces)

Lectures 2 & 3 (9 & 11 Sept) Steenrod I, Fomenko 1.5 (covering homotopy theorem), Husemoller I, Guillemin & Sternberg 1.2, Milnor, Milnor & Stasheff 5 & 6 (classifying spaces)

Lecture 4 (16 Sept) The above, plus Hatcher 3.5 (cellular cohomology), 3F (direct limits), 4.1 (cellular approximation), Stasheff, Mac Lane (group cohomology), Atiyah & Bott or Guillemin & Sternberg (equivariant cohomology)

Lectures 5 & 6 (18 & 23 Sept) Hatcher's unpublished manuscript, Bott & Tu, Fomenko et al. (spectral sequences)

Lecture 7 (30 Sept) Bröcker & tom Dieck IV.1 (Weyl group), Bott & Tu 11 (Lefschetz fixed point theorem), Borel LNM 36 (cohomology of classifying spaces and homogeneous spaces)

Lecture 8 (2 Oct) Bröcker & tom Dieck IV.2 (maximal tori), Bott & Tu 21 (flag bundles), Spanier 5.9 (Hopf algebras),

Lecture 9 (7 Oct) Bröcker & tom Dieck V.1-2 (generation of Weyl group by reflections), Helgason, Bourbaki (Chevalley's theorem)

Lecture 10 (14 Oct) Borel L.A.G., Macdonald's chapter in Carter et al. (generalities on algebraic groups and homogeneous spaces), Macdonald's chapter in Atiyah et al., Chevalley VI, Bröcker & tom Dieck III.8 (complexification)

Lectures 11 & 12 (16 & 21 Oct) Borel L.A.G., Macdonald's chapter in Carter et al. (actions of solvable groups, Lie-Kolchin theorem, Borel subgroups, existence of homogeneous spaces, projectivity of G/B, affineness of G/H for H normal), Mumford et al., Hochschild (reductive and compact groups).

Lecture 13 (23 Oct) Bröcker & tom Dieck V (root systems), Borel PNAS (reductive vs. compact homogeneous spaces)

Lecture 14 (28 Oct) Borel L.A.G. (fixed points of group actions on G/B, etc.), Bialynicki-Birula (decomposition theorem)

Lectures 15 & 16 (30 Oct & 6 Nov) Borel L.A.G. (Bruhat decomposition), Kumar, Humphreys, Bourbaki (ordering on the Weyl group)

Lectures 17, 18, 19... (11, 13, 18 Nov...) Bernstein-Gelfand-Gelfand

Last two lectures (9 & 11 Dec) Segal's chapter in Carter et al. (Borel-Weil), Bott, Demazure (Borel-Weil-Bott)