2024/06/28 by Jonas T. Hartwig, Hartwig, Jonas T. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2406.20012
openalex publication_date 2024/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Galois orders, introduced by Futorny and Ovsienko, is a class of noncommutative algebras that includes generalized Weyl algebras, the enveloping algebra of the general linear Lie algebra and many others. We prove that the noncommutative Kleinian singularities of type D can be realized as principal Galois orders. Our starting point is an embedding theorem due to Boddington. We also compute explicit generators for the corresponding (Morita equivalent) flag order, as a subalgebra of the nil-Hecke algebra of type A1(1). Lastly, we compute structure constants for Harish-Chandra modules of local distributions and give a visual description of their structure from which subquotients are easily obtained.