Macdonald polynomials and BGG reciprocity for current algebras

• Matthew Bennett ^[5] ; Arkady Berenstein ^[3] ; Vyjayanthi Chari ^[4] ; Anton Khoroshkin ^[1] ; Sergey Loktev ^[2]
  1. [1] Stony Brook University

     Stony Brook University

     Town of Brookhaven, Estados Unidos

     
  2. [2] Higher School of Economics, National Research University

     Higher School of Economics, National Research University

     Rusia

     
  3. [3] University of Oregon
  4. [4] University of California
  5. [5] IMECC-UNICAMP

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 20, Nº. 2, 2014, págs. 585-607
• Idioma: inglés
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• Resumen

  • We study the category IgrIgr of graded representations with finite-dimensional graded pieces for the current algebra g⊗C[t]g⊗C[t] where gg is a simple Lie algebra. This category has many similarities with the category OO of modules for gg , and in this paper, we prove an analog of the famous BGG duality in the case of sln+1sln+1 .