2017/09/05 by Nick Early, Early, Nick, Volodymyr Mazorchuk +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Medicine · #Amyloidosis: Diagnosis, Treatment, Outcomes #FOS: Mathematics #Peptidase Inhibition and Analysis #Protein Tyrosine Phosphatases #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1709.01553
openalex publication_date 2017/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that every orthogonal Gelfand-Zeitlin algebra U acts on its\nGelfand-Zeitlin subalgebra \Γ. Considering the dual module, we show that\nevery Gelfand-Zeitlin character of \Γ is realizable in a U-module. We\nobserve that the Gelfand-Zeitlin formulae can be rewritten using divided\ndifference operators. It turns out that the action of the latter operators on\n\Γ gives rise to an explicit basis in a certain Gelfand-Zeitlin submodule\nof the dual module mentioned above. This gives, generically, both in the case\nof regular and singular Gelfand-Zeitlin characters, an explicit construction of\nsimple modules which realize given Gelfand-Zeitlin characters.\n