Artículos de revistas
Macdonald Polynomials And Bgg Reciprocity For Current Algebras
Registro en:
Selecta Mathematica, New Series. Birkhauser Verlag Ag, v. 20, n. 2, p. 585 - 607, 2014.
10221824
10.1007/s00029-013-0141-7
2-s2.0-84896400132
Autor
Bennett M.
Berenstein A.
Chari V.
Khoroshkin A.
Loktev S.
Institución
Resumen
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. © 2013 Springer Basel. 20 2 585 607 NSh-3349.2012.2; SF; Simons Foundation; RFBR-10-01-00836; SF; Simons Foundation; RFBR-CNRS-10-01-93111; SF; Simons Foundation; RFBR-CNRS-10-01-93113; SF; Simons Foundation Ardonne, E., Kedem, R., Fusion products of Kirillov-Reshetikhin modules and fermionic multiplicity formulas (2007) J. Algebra, 308, pp. 270-294 Bennett, M., Chari, V., Tilting modules for the current algebra of a simple Lie algebra (2012) Recent developments in Lie algebras, groups and representation theory. In: Proceedings of Symposia in Pure Mathematics, AMS Bennett, M., Chari, V., Manning, N., BGG reciprocity for current algebras Adv. Math., 231 (1), pp. 276-305 Chari, V., Fourier, G., Khandai, T., A categorical approach to Weyl modules (2010) Transf. Groups, 15 (3), pp. 517-549 Chari, V., Greenstein, J., Current algebras, highest weight categories and quivers (2007) Adv. Math., 216 (2), pp. 811-840 Chari, V., Loktev, S., Weyl, Demazure and fusion modules for the current algebra of slr+1 (2006) Adv. Math., 207, pp. 928-960 Chari, V., Pressley, A., Weyl modules for classical and quantum affine algebras (2001) Represent. Theory, 5, pp. 191-223. , (electronic) Di Francesco, P., Kedem, R., Proof of the combinatorial Kirillov-Reshetikhin conjecture (2008) Int. Math. Res. Notices, , doi: 10. 1093/imrn/rnn006 Donkin, S., Tilting modules for algebraic groups and finite dimensional algebras. A handbook of tilting theory (2007) Lond. Math. Soc. Lect. Notes, 332, pp. 215-257 Fourier, G., Littelmann, P., Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2007) Adv. Math., 211 (2), pp. 566-593 Ion, B., Nonsymmetric Macdonald polynomials and Demazure characters (2003) Duke Math. J., 116 (2), pp. 299-318 Macdonald, I.G., (1979) Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, , Oxford: Clarendon Press Naoi, K., Fusion products of Kirillov-Reshetikhin modules and the X = M conjecture (2012) Adv. Math., 231, pp. 1546-1571 Sanderson, Y., On the connection between Macdonald polynomials and Demazure characters (2000) J. Algebraic Comb., 11, pp. 269-275