BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Claire Frechette (BC) DTSTART:20230406T185000Z DTEND:20230406T195000Z DTSTAMP:20260423T022918Z UID:GPRTatNU/71 DESCRIPTION:Title: Metaplectic ice: using statistical mechanics in representation theory\nby Claire Frechette (BC) as part of Geometry\, Physics\, and Representa tion Theory Seminar\n\n\nAbstract\nLocal 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 red uctive groups are replaced by their metaplectic covering groups. We will e xamine these functions for covers of $GL_r$ through the lens of a solvable lattice model\, or ice model: a construction from statistical mechanics t hat provides a surprising bridge between spaces of Whittaker functions and representations of quantum groups. This story has been well studied befor e 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 cove r of $GL_r$\, as well as examine how different choices of covering group i nteract with the center of $GL_r$ to change the story.\n LOCATION:https://researchseminars.org/talk/GPRTatNU/71/ END:VEVENT END:VCALENDAR