Claire Frechette

Abstract:  Local Whittaker functions for principal series representations of reductive groups play an integral role in number theory and representation theory, and many of their applications extend to the metaplectic case, where reductive groups are replaced by their metaplectic covering groups. We will examine metaplectic Whittaker functions for covers of GL_r through the lens of a solvable lattice model, or ice model: a construction from statistical mechanics that provides a surprising bridge between spaces of Whittaker functions and representations of quantum groups. This story has been well studied before for the case of one particularly nice cover of GL_r, which eliminates complications arising from the center of the group. In this talk, we will show that the same types of connections hold for any metaplectic cover of GL_r, as well as examine how different choices of covering group interact with the center of GL_r to change the story.