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

Mathematics – Representation Theory

Scientific paper

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15 pages, 3 figures, submitted

Scientific paper

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 $2\times 2$ 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.

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