1 January - 19 June 1997
Organisers: M.Broue (Paris), R.W. Carter (Warwick), J Saxl (Cambridge)
Aims: To survey the current understanding of the irreducible representations of reductive algebraic groups in the algebraically closed field over which the group is defined. Particular attention will be paid to Lusztig's conjectured character formula for such representations. Applications to the representation theory of related finite groups will also be considered, as will applications to the subgroup structure of algebraic groups.
Participants: The ASI is aimed at research mathematicians at postdoctoral level and beyond, but will also be accessible to good research students.
HH Andersen (Aarhus), M Broué (Paris), RW Carter (Warwick), J Saxl (Cambridge)
Arrival day: Monday 23 June 1997
15.00 - 18.00 Registration
15.30 Tea
Day 1 - Tuesday 24 June
08.30 - 09.00 Registration
09.00 - 10.00 R W Carter: Introduction to the representation theory of algebraic groups
Coffee
10.30 - 11.30 P Littelmann: Paths and bases for irreducible modules
11.35 - 12.35 J E Humphreys: An overview of tilting modules
Lunch
14.00 - 15.00 Informal discussion
Tea
16.00 - 17.00 G R Robinson: Arithmetical properties of blocks
17.05 - 18.05 G D James: Symmetric groups and Schur algebras
19.00 Dinner
Day 2 - Wednesday 25 June
09.00 - 10.00 R W Carter: Introduction to the representation theory of algebraic groups
Coffee
10.30 - 11.30 G Lusztig : Algebraic groups and finite Coxeter groups
11.35 - 12.35 M Brou\'e
Spetsoids
Lunch
14.00 - 15.00 Informal discussion
Tea
16.00 - 17.00 J-P Serre: Complete reducibility for spherical buildings and reductive groups
17.05 - 18.05 P Littelmann: Paths and bases for irreducible modules
18.05 Reception in the Newton Institute
19.00 Dinner
Day 3 - Thursday 26 June
09.00 - 10.00 G D James: Symmetric groups and Schur algebras
Coffee
10.30 - 11.30 G Lusztig: Constructible functions on the Steinberg variety
11.35 - 12.35 T Tanisaki: Highest weight modules associated to Hermitian symmetric spaces
Lunch
14.00 - 15.00 Informal discussion
Tea
16.00 - 17.00 J-P Serre: Complete reducibility for spherical buildings and reductive groups
17.05 - 18.05 G R Robinson: Arithmetical properties of blocks
19.00 Dinner
Day 4 - Friday 27 June
09.00 - 10.00 H H Andersen: Tilting modules for algebraic groups
Coffee
10.30 - 11.30 G Lusztig: Periodic W-graphs
11.35 - 12.35 A Premet: Support varieties, stabilizers of linear forms, and representation type
Lunch
14.00 - 15.00 Informal discussion
Tea
16.00 - 17.00 J-P Serre: Complete reducibility for spherical buildings and reductive groups
17.05 - 18.05 F Digne: Cohomology of some Deligne-Lusztig varieties
19.00 Dinner
Day 5 - Saturday 28 June
09.00 - 10.00 P Littelmann: Paths and bases for irreducible modules
Coffee
10.30 - 11.30 S Donkin: Some exact sequences of rational modules for algebraic groups
11.35 - 12.35 G R Robinson: Arithmetical properties of blocks
Lunch
Afternoon Free
19.00 Dinner
Day 6 - Sunday 29 June
There will be no lectures. There will be an excursion by coach to Isaac Newton's birthplace, Woolsthorpe Manor, and Lincoln Cathedral for those who wish to take part.
Day 7 - Monday 30 June
09.00 - 10.00 M Aschbacher: Quasithin groups
Coffee
10.30 - 11.30 R Lyons: Revision of the classification of finite simple groups
11.35 - 12.35 A Kleshchev: Some problems on the finite and finitary symmetric groups
Lunch
14.00 - 15.00 Informal discussion
Tea
16.00 - 17.00 P Fong: Shintani descent and perfect isometries in linear groups
17.05 - 18.05 G McNinch: Results relating representation dimensions to semi-simplicity
18.15 Reception hosted by Cambridge University Press
19.45 Dinner
Day 8 - Tuesday 1 July
09.00 - 10.00 G M Seitz: Double cosets in algebraic groups
Coffee
10.30 - 11.30 J-P Serre: Some finite subgroups of Lie groups
11.35 - 12.35 M W Liebeck: Subgroups of exceptional groups
Lunch
Afternoon Free
19.00 Dinner
Day 9 - Wednesday 2 July
09.00 - 10.00 M Aschbacher: Quasithin groups
Coffee
10.30 - 11.30 R Lyons: Revision of the classification of finite simple groups
11.35 - 12.35 A Kleshchev: Some problems on the finite and finitary symmetric groups
Lunch
14.00 - 15.00 R M Guralnick: Some applications of subgroup structure
Tea
16.00 - 18.05 Contributed Lectures
16.00 R Gow: Some properties of Steinberg lattices of groups of Lie type
16.40 K Magaard: On maximal subgroups of classical groups
17.20 P H Tiep: Low-dimensional representations of finite classical groups
19.00 for 19.30 Conference Dinner at Emmanuel College
Day 10 - Thursday 3 July
09.00 - 10.00 G M Seitz: Double cosets in algebraic groups
Coffee
10.30 - 11.30 J-P Serre: Some finite subgroups of Lie groups
11.35 - 12.35 M W Liebeck: Subgroups of exceptional groups
Lunch
14.00 - 15.00 R Steinberg: The isomorphism and isogeny theorems for reductive algebraic groups
Tea
16.00 - 18.05 Contributed Lectures
16.00 G R\"ohrle: Parabolic subgroups and orbits
16.40 I D Suprunenk: op-large representations and asymptotics
17.20 J Brundan: Dense orbits and double cosets
19.00 Dinner
Day 11 - Friday 4 July
09.00 - 10.00 M Aschbacher: Quasithin groups
Coffee
10.30 - 11.30 J Saxl: Overgroups of special elements
11.35 - 12.35 A Kleshchev: Some problems on the finite and finitary symmetric groups
Lunch
14.00 - 15.00 G M Seitz: Double cosets in algebraic groups
16.00 - 17.00 A Borovik: Group of finite Morley rank
17.05 - 18.05 L L Scott: to be announced
18.05 Reception in the Newton Institute
19.00 Dinner and departure