2024/11/21 by Lewis Dean, Dean, Lewis
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2411.14170
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the Demazure product in a double affine setting. Work by Muthiah and Puskás gives a conjectural way to define this in terms of the q=0 specialisation of these Hecke algebras. We instead take a different approach generalising work by Felix Schremmer, who gave an equivalent formula for the (single) affine Demazure product in terms of the quantum Bruhat graph. We focus on type \widehatSL2, where we prove that the quantum Bruhat graph of this type satisfies some nice properties, which allows us to construct a well-defined associative Demazure product for the double affine Weyl semigroup WT (for level greater than one). We give results regarding the Demazure product and Muthiah and Orr's length function for WT, and we verify that our proposal matches specific examples computed by Muthiah and Puskás using the Kac-Moody affine Hecke algebra