"L-functions 'vast generalizations of the Riemann zeta function' are fundamental objects of study in number theory. In the 1980's the idea emerged that it could be useful to tie together a family of related L-functions in one variable to create a ""double Dirichlet series,"" which could be used to study the average behavior of the original family of L-functions. Double Dirichlet series soon became multiple Dirichlet series. It has gradually emerged that the local structure of these multiple Dirichlet series shows a rich connection to combinatorial representation theory.This program will explore this interface between automorphic forms and combinatorial representation theory, and will develop computational tools for facilitating investigations. On the automorphic side, Whittaker functions on p-adic groups and their covers are the fundamental objects. Whittaker functions and their relatives are expressible in terms of combinatorial structures on the associated L-group, its flag variety, or Schubert varieties. In the combinatorial theory crystal graphs, Demazure characters, the Schubert calculus and Kazhdan-Lusztig theory all enter.