4 papers · 1 filter
Metaplectic Covers of -adic Groups and Quantum Groups at Roots of Unity
Valentin Buciumas, Manish M. Patnaik
We describe the structure of the Whittaker or Gelfand-Graev module on a -fold metaplectic cover of a -adic group at both the Iwahori and spherical level. We express our a…
Colored Vertex Models and Iwahori Whittaker Functions
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
We give a recursive method for computing all values of a basis of Whittaker functions for unramified principal series invariant under an Iwahori or parahoric subgroup of a split re…
Polynomial functors and two-parameter quantum symmetric pairs
Valentin Buciumas, Hankyung Ko
We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial representations of the general…
Vertex operators, solvable lattice models and metaplectic Whittaker functions
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
We show that spherical Whittaker functions on an -fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl…