21 citations · 89 across the 16 of their papers we have counts for
16 papers
Quantum wreath products and -adic general linear group
Valentin Buciumas, Chun-Ju Lai
We study the pro- Iwahori-Hecke algebra and its Gelfand-Graev modules for the -adic general linear group and its metaplectic covers. We develop the theory of quantum wreath p…
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…
Iwahori-metaplectic duality
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
We construct a family of solvable lattice models whose partition functions include -adic Whittaker functions for general linear groups from two very different sources: from Iwah…
Quasi-solvable lattice models for and Demazure atoms and characters
Valentin Buciumas, Travis Scrimshaw
We construct colored lattice models whose partition functions represent symplectic and odd orthogonal Demazure characters and atoms. We show that our lattice models are not solvabl…
Metaplectic Iwahori Whittaker functions and supersymmetric lattice models
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
In this paper we compute new values of Iwahori Whittaker functions on -fold metaplectic covers of with a split reductive group over…
Double Grothendieck polynomials and colored lattice models
Valentin Buciumas, Travis Scrimshaw
We construct an integrable colored six-vertex model whose partition function is a double Grothendieck polynomial. This gives an integrable systems interpretation of bumpless pipe d…
Colored five-vertex models and Lascoux polynomials and atoms
Valentin Buciumas, Travis Scrimshaw, Katherine Weber
We construct an integrable colored five-vertex model whose partition function is a Lascoux atom based on the five-vertex model of Motegi and Sakai [arXiv:1305.3030] and the colored…
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…
Colored five-vertex models and Demazure atoms
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
Type A Demazure atoms are pieces of Schur functions, or sets of tableaux whose weights sum to such functions. Inspired by colored vertex models of Borodin and Wheeler, we will cons…
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…
Duality for metaplectic ice
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
We interpret values of spherical Whittaker functions on metaplectic covers of the general linear group over a nonarchimedean local field as partition functions of two different sol…
Quantum polynomial functors from -Hecke pairs
Valentin Buciumas, Hankyung Ko
We define a new category of quantum polynomial functors extending the quantum polynomials introduced by Hong and Yacobi. We show that our category has many properties of the catego…
Hecke Modules from Metaplectic Ice
Ben Brubaker, Valentin Buciumas, Daniel Bump +1
We present a new framework for a broad class of affine Hecke algebra modules, and show that such modules arise in a number of settings involving representations of -adic groups…
A Yang-Baxter equation for metaplectic ice
Ben Brubaker, Valentin Buciumas, Daniel Bump
We will give new applications of quantum groups to the study of spherical Whittaker functions on the metaplectic -fold cover of , where is a nonarchimedean local fi…
Quantum groups obtained from solutions to the parametrized Yang-Baxter equation
Valentin Buciumas
In this article we use a parametrized version of the FRT construction to construct two new coquasitriangular Hopf algebras. The first one, , is a quantization of…