Two proofs of a Jantzen Conjecture for Whittaker modules

• Jens Niklas Eberhardt ^[1] ; Anna Romanov ^[2]
  1. [1] Johannes Gutenberg University of Mainz

     Johannes Gutenberg University of Mainz

     Kreisfreie Stadt Mainz, Alemania

     
  2. [2] University of New South Wales, Sydney, Australia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01057-2
• Enlaces
  • Texto completo
• Resumen

  • We define a filtration of a standard Whittaker module over a complex semisimple Lie algebra and and establish its fundamental properties. Our filtration specializes to the Jantzen filtration of a Verma module for a certain choice of parameter. We prove that embeddings of standard Whittaker modules are strict with respect to our filtration, and that the filtration layers are semisimple. This provides a generalization of the Jantzen conjectures to Whittaker modules. We prove these statements in two ways. First, we give an algebraic proof which compares Whittaker modules to Verma modules using a functor introduced by Backelin. Second, we give a geometric proof using mixed twistor D-modules.

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