On Products of Random Matrices and certain Hecke Algebras associated with Groups of $2\times 2$ Matrices

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/115461The 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 $2\times 2$ 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 $2\times 2$ matrices.15 pages, 3 figures, submittedRepresentation TheoryProbability20E45, 22E46, 43A90, 53C35On Products of Random Matrices and certain Hecke Algebras associated with Groups of $2\times 2$ Matricestext