My research interests lie on the boundary of Number Theory and Combinatorial Representation Theory. For example, I am interested in questions related to the study of Whittaker functions on metaplectic covers of nonarchimedean groups. Recently with my collaborators we extended the study of Iwahori-Whittaker functions to metaplectic covers of Kac-Moody groups, and studied properties of related correction factors. The main tools of this study are Demazure and Demazure-Lusztig operators, highest weight crystals and other combinatorial devices associated with the representation theory of finite and infinite-dimensional Lie algebras. Similar devices, related to symmetries and the Bruhat order of a Weyl group appear in the study of a wide range of interesting questions.