2023/10/20 by Gufang Zhao, Zhao, Gufang, Changlong Zhong +1
Mathematics · #14F08 #16T20 #17B37 #20G42 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2310.13460
openalex publication_date 2023/10/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Associated to any root datum, there is an elliptic affine Hecke algebra defined by Ginzburg, Kapranov, and Vasserot. In this study, we establish a Fourier-Mukai functor from the representation category of the elliptic affine Hecke algebra to the corresponding category associated with the Langlands dual root datum. To achieve this connection, we employ the elliptic Hecke algebra with dynamical parameters as an intermediary.