My research interests lie in the representation theory of finite groups of Lie type, particularly the groups GL_n over finite principal ideal local rings.
My work focuses on the computation of Whittaker models of representations of groups of the form GL_n(O_l), where O_l is a finite principal ideal local ring, i.e. is isomorphic to Z/(p^l Z), with p being a prime number. Moreover, I study decompositions of principal series representations, Whittaker models, and branching problems for these groups. A major aspect of my work involves determining the irreducible constituents of induced representations, studying their dimensions and multiplicities, and understanding the structure of Whittaker models associated to these representations.
Moreover, representation theory has deep connections and applications across several areas of mathematics and the sciences, including signal and image processing, coding theory, and network security.