Colored five-vertex models and Demazure atoms

Abstract

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 construct solvable lattice models whose partition functions are Demazure atoms; the proof of this makes use of a Yang-Baxter equation for a colored five-vertex model. As a biproduct, we construct Demazure atoms on Kashiwara's ${\mathcal{B}}_{\infty }$ crystal and give new algorithms for computing Lascoux-Schützenberger keys.

References in corpus (13)

• Another proof of the alternating sign matrix conjecture
• Quantum Integrability and Generalised Quantum Schubert Calculus
• A Decomposition of Schur functions and an analogue of the Robinson-Schensted-Knuth Algorithm
• Between the stochastic six vertex model and Hall-Littlewood processes
• A Demazure crystal construction for Schubert polynomials
• A Yang-Baxter equation for metaplectic ice
• Keys and alternating sign matrices
• Schubert puzzles and integrability I: invariant trilinear forms
• Colour-independent partition functions in coloured vertex models
• Colored Vertex Models and Iwahori Whittaker Functions
• Keys and Demazure crystals for Kac-Moody algebras
• Yang-Baxter algebras as convolution algebras: The Grassmannian case
• Symplectic keys and Demazure atoms in type C

Cited by in corpus (4)

• Colored Vertex Models and Iwahori Whittaker Functions
• Keys and Demazure crystals for Kac-Moody algebras
• $B_k$ Spin Vertex Models and Quantum Algebras
• Equivalences of LLT polynomials via lattice paths