On the Bott-Borel-Weil theorem (Q2473720)

The classical Bott-Borel-Weil theorem describes the dimension of the cohomology of the nilradical of the Borel subalgebra of the classical simple Lie algebra \(\mathfrak g\) with coefficients in an irreducible \(\mathfrak g\)-module, in terms of the corresponding Weyl group. However, the description of the cohomology itself, though known in many particular cases, remains unknown in general. Here the author considers the case of the trivial module. He determines the explicit basis of the corresponding cohomology and describes, up to sign, its commutative superalgebra structure. The translation of the paper, as it unfortunately often happens, is poor. However, this should not pose any problem to a specialist.