6 papers
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…