Department of Mathematics - Master Calendar

I will give an exposition of a celebrated series of papers by the three referenced authors. They proved that if G is a semisimple algebraic group over a field of characteristic 0 and if {I_λ : λ ∈ Λ} is a set of representatives of the isomorphism classes of irreducible representations of G then the coordinate ring of G is the direct sum k[G] = \bigoplus_{λ∈Λ} I_λ ⊗k I*_λ. The proof uses mostly elementary notions such as the left and right translation actions on k[G] and the notion of the matrix coefficients of an algebraic representation.