Prime ideals in the quantum grassmannian

• S. Launois ^[1] ; T. H. Lenagan ^[2] ; L. Rigal ^[3]
  1. [1] University of Kent

     University of Kent

     City of Canterbury, Reino Unido

     
  2. [2] University of Edinburgh

     University of Edinburgh

     Reino Unido

     
  3. [3] Université Jean-Monnet

  Mostrar afiliaciones +
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 4, 2008, págs. 697-725
• Idioma: inglés
• DOI: 10.1007/s00029-008-0054-z
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We consider quantum Schubert cells in the quantum grassmannian and give a cell decomposition of the prime spectrum via the Schubert cells. As a consequence, we show that all primes are completely prime in the generic case where the deformation parameter q is not a root of unity. There is a natural torus action of H = (k ∗ ) n on the quantum grassmannian Oq(Gm,n(k)) and the cell decomposition of the set of H-primes leads to a parameterisation of the H-spectrum via certain diagrams on partitions associated to the Schubert cells. Interestingly, the same parameterisation occurs for the nonnegative cells in recent studies concerning the totally nonnegative grassmannian. Finally, we use the cell decomposition to establish that the quantum grassmannian satisfies normal separation and catenarity.