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: o*p-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