2023/03/01 by Evgeny Feigin, Feigin, Evgeny, Ievgen Makedonskyi +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2303.00241
openalex publication_date 2023/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The t=0 specialization of the Mimachi-Noumi Cauchy-type identity rewrites certain infinite product in terms of specialized nonsymmetric Macdonald polynomials of type GLn. We interpret the infinite product as a character of the space of functions on a certain matrix space. We show that the space of functions admits a filtration such that the graded pieces are isomorphic to the tensor products of certain generalized global Weyl modules of the Iwahori algebra. We identify the characters of the graded pieces with the terms of the specialized Mimachi-Noumi formula. We conjecture the existence of an analogous filtration on the space of functions on the Iwahori group for all simple Lie algebras and prove the conjecture for SLn. Our construction can be seen as a current algebra extension of the van der Kallen filtration on functions on a Borel subgroup.