Interview with Solomon Friedberg on Weyl group multiple Dirichlet series: Type A combinatorial theory, by Ben Brubaker, Daniel Bump, and Solomon Friedberg
Professor Friedberg discusses the innovative and collaborative path that led to the discoveries described in this book and their potential long-term consequences. "Weyl group multiple Dirichlet series" are generalizations of the classical Riemann zeta function, a function defined in the 19th century whose ongoing study is central in analytic number theory. Like the Riemann zeta function, the series studied here are Dirichlet series with analytic continuation and functional equations. However, Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics... The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.