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Learn about the construction of irreducible representations of GL_3(O) in this 54-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 particular focus on zeta and L-functions. Discover the significance of Dirichlet's zeta function in enumerating number field ideals, Witten's zeta function in counting Lie group representations, and Hasse-Weil zeta functions in encoding rational points of algebraic varieties over finite fields. Examine how zeta functions of groups and rings serve as essential tools in asymptotic theory, featuring Euler product decompositions with rational local factors that reveal underlying structural patterns. Delivered by Pooja Singla as part of a broader program bringing together experts in zeta functions, combinatorial areas, and enumerative algebra to address outstanding problems in the field.
