Metaplectic ice: using statistical mechanics in representation theory

Abstract: Local Whittaker functions for 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 these 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 all complications arising from the center of the group. In this talk, we will see 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.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

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