The affine VW supercategory

• M. Balagovic ^[1] ; Z. Daugherty ^[2] ; I. Entova-Aizenbud ^[7] ; I. Halacheva ^[3] ; J. Hennig ^[8] ; M. S. Im ^[4] ; G. Letzter ^[9] ; E. Norton ^[5] ; V. Serganova ^[10] ; C. Stroppel ^[6]
  1. [1] Newcastle University

     Newcastle University

     Reino Unido

     
  2. [2] City College of New York

     City College of New York

     Estados Unidos

     
  3. [3] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
  4. [4] United States Military Academy

     United States Military Academy

     Town of Highlands, Estados Unidos

     
  5. [5] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
  6. [6] University of Bonn

     University of Bonn

     Kreisfreie Stadt Bonn, Alemania

     
  7. [7] Ben-Gurion University, Israel
  8. [8] Center for Communications Research, USA
  9. [9] Department of Defense, USA
  10. [10] University of California at Berkeley, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 26, Nº. 2, 2020
• Idioma: inglés
• DOI: 10.1007/s00029-020-0541-4
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• Resumen

  • We define the affine VW supercategory , which arises from studying the action of the periplectic Lie superalgebra p(n) on the tensor product M⊗V⊗a of an arbitrary representation M with several copies of the vector representation V of p(n). It plays a role analogous to that of the degenerate affine Hecke algebras in the context of representations of the general linear group; the main obstacle was the lack of a quadratic Casimir element in p(n)⊗p(n). When M is the trivial representation, the action factors through the Brauer supercategory sBr. Our main result is an explicit basis theorem for the morphism spaces of and, as a consequence, of sBr. The proof utilises the close connection with the representation theory of p(n). As an application we explicitly describe the centre of all endomorphism algebras, and show that it behaves well under the passage to the associated graded and under deformation.