On Products of Random Matrices and certain Hecke Algebras associated with Groups of 2× 2 Matrices

الأصل · EN

The determination of the density functions for products of random elements from specified classes of matrices is a basic problem in random matrix theory and is also of interest in theoretical physics. For connected simple Lie groups of 2× 2 matrices and conjugacy and spherical classes a complete solution is given here. The problem/solution can be re-stated in terms of the structure of certain Hecke algebras attached to groups of 2× 2 matrices.