3 Review(s)

The course given by the author at the Tata Institute in 1992explains the solution by O. Mathieu of some conjectures inthe representation theory of arbitrary semisimple algebraicgroups. The conjectures concern filtrations of (tensorproducts of) "standard" representations; while Demazurestudied the representations by means of a particularresolutionof singularities of Schubert varieties, themethod of Mathieu involves sheafcohomology and "Frobeniussplittings" on a Demazure resolution in finitecharacteristic p. The notes explain all this, but assumesome familiarity with algebraic varieties and semisimplealgebraic groups (or Liegroups).