Isaac Newton Institute for Mathematical Sciences

Representation Theory of Algebraic Groups and Related Finite Groups

1 January - 19 June 1997

Organisers: M.Broue (Paris), R.W. Carter (Warwick), J Saxl (Cambridge)

A NATO Advanced Study Institute

with additional support from the European Union

MODULAR REPRESENTATION THEORY AND SUBGROUP STRUCTURE OF ALGEBRAIC GROUPS AND RELATED FINITE GROUPS

23 June - 4 July 1997

At the Newton Institute, Cambridge, UK

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.

Poster Sessions

Organising Committee:

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

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