1 January - 19 June 1997

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

There is a famous formula, due to Hermann Weyl, for the characters of the finite dimensional irreducible modules for simple algebraic groups over the field of complex numbers. This has found many and varied applications ever since its discovery. If instead we consider such groups over fields of positive characteristic p the situation is more complicated. A main aim is to find an analogue in this situation of Weyl's formula. There is a conjectured character formula due to G.Lusztig. This has now been established for all primes p "sufficiently large"; on the other hand for no fixed particular value of p is the conjecture known to hold! One of the main themes of the meeting will be to clarify the situation regarding Lusztig's conjecture. Another will be to investigate the irreducible representations of the corresponding finite groups of Lie type (i.e. algebraic groups over finite fields) where the characteristic of the representation is a prime which is not necessarily equal to the characteristic of the group. The subgroup structure of the algebraic groups and related finite groups is closely connected to this representation theory, and will be another theme for investigation.