Kac-Moody algebras and the cde-triangle
  This is the written version of a talk at the conference on ``Non-commutative geometry and representation theory in mathematical physics'' held in Karlstad, Sweden, 5--10 July, 2004. In it we show that the duality formula of Rocha-Caridi and Wallach is a simple consequence of the so called cde-triangle of modular representation theory. It tries to reflect the attempt of the talk to cater to the differing backgrounds of its listeners. 
Torsten Ekedahl