Macdonald polynomials and BGG reciprocity for current algebras

Matthew Bennett, Arkady Berenstein, Vyjayanthi Chari, Anton Khoroshkin, Sergey Loktev

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)585-607
Number of pages23
JournalSelecta Mathematica, New Series
Issue number2
StatePublished - Apr 2014
Externally publishedYes

Bibliographical note

Funding Information:
A.B. was partially supported by DMS-0800247 and DMS-1101507. V.C. was partially supported by DMS-0901253. S.L. was partially supported by RFBR-CNRS-11-01-93105 and RFBR-12-01-00944. A.K was supported by the grants NSh-3349.2012.2, RFBR-10-01-00836, RFBR-CNRS-10-01-93111, RFBR-CNRS-10-01-93113, and by the Simons Foundation.

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


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