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Macdonald polynomials and BGG reciprocity for current algebras |
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| Authors: | Matthew Bennett Arkady Berenstein Vyjayanthi Chari Anton Khoroshkin Sergey Loktev |
| Affiliation: | 1. IMECC-UNICAMP Rua Sergio Buarque de Hollanda, 651 Barao Geraldo, Campinas, SP, 13083-859, Brazil 3. Department of Mathematics, University of Oregon, Eugene, OR, 97403, USA 2. Department of Mathematics, University of California, Riverside, CA, 92521, USA 4. Simons Center for Geometry and Physics, Stony Brook University, Stony Brook, NY, 11794, USA 5. National Research University Higher School of Economics, 7 Vavilova Str., Moscow, Russia |
| Abstract: | We study the category $mathcal I _{mathrm{gr }}$ of graded representations with finite-dimensional graded pieces for the current algebra $mathfrak{g }otimes mathbf{C }[t]$ where $mathfrak{g }$ is a simple Lie algebra. This category has many similarities with the category $mathcal O $ of modules for $mathfrak{g }$ , and in this paper, we prove an analog of the famous BGG duality in the case of $mathfrak{sl }_{n+1}$ . |
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