In the seminar we want to study the Satake-Isomorphism, and in particular its integral variant that relates to the so-called Vinberg monoid. The Satake-isomorphism is a classical and well understood construction in the representation theory of p-adic Lie groups G, such as GL_n(Q_p). It identifies the spherical Hecke algebra of G (that controls the unramified representations of G) with an explicit algebra of Laurent polynomials. In the seminar we want to introduce and study these objects as well as the Satake-isomorphism in the classical case (i.e. over an algebraically closed field of characteristic zero); and then move to the case of integral coefficients, where the story is more complicated and the result is formulated in terms of the Vinberg monoid.

Kurs im HIS-LSF