Frobenius Splittings and B-modules

The course given by the author at the Tata Institute in 1992
explains the solution by O. Mathieu of some conjectures in
the representation theory of arbitrary semisimple algebraic
groups. The conjectures concern filtrations of (tensor
products of) "standard" representations; while Demazure
studied the representations by means of a particular
resolutionof singularities of Schubert varieties, the
method of Mathieu involves sheafcohomology and "Frobenius
splittings" on a Demazure resolution in finite
characteristic p. The notes explain all this, but assume
some familiarity with algebraic varieties and semisimple
algebraic groups (or Liegroups).