A Combinatorial Formula for the Wedderburn Decomposition of Rational Group Algebras

Learn about the Wedderburn decomposition of rational functions in this 22-minute lecture from the Combinatorial Methods in Enumerative Algebra program at the International Centre for Theoretical Sciences. Explore how algebraic counting problems generate integer sequences and their encoding through generating functions, with a focus on zeta and L-functions. Discover the connections between Dirichlet's zeta function, Witten's zeta function, and Hasse-Weil zeta functions in enumerating mathematical structures. Examine how zeta functions of groups and rings serve as tools in asymptotic theory, featuring Euler product decompositions with rational local factors. Delivered as part of a broader program bringing together experts in zeta functions and combinatorial areas, this lecture contributes to the understanding of enumerative algebra and its applications in group and ring theory.