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ISSN 1088-4165

-analogs of -characters of Kirillov-Reshetikhin modules of quantum affine algebras

Author(s): Hiraku Nakajima
Journal: Represent. Theory 7 (2003), 259-274.
MSC (2000): Primary 17B37; Secondary 81R50, 82B23
Posted: July 10, 2003
MathSciNet review: 1993360
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Abstract: We prove the Kirillov-Reshetikhin conjecture concerning certain finite dimensional representations of a quantum affine algebra ${\mathbf U}_q(\widehat{\mathfrak g})$ when $\widehat{\mathfrak g}$ is an untwisted affine Lie algebra of type . We use -analog of -characters introduced by the author in an essential way.

References:

1.: V. Chari, Braid group actions and tensor products, Int. Math. Res. Not. 2002, no. 7, 357-382. MR 2003a:17014
2.: V. Chari and A. Pressley, Quantum affine algebras and their representations, in Representations of groups (Banff, AB, 1994), Amer. Math. Soc., Providence, RI, 1995, pp. 59-78. MR 96j:17009
3.: V.G. Drinfel'd, A new realization of Yangians and quantized affine algebras, Soviet math. Dokl. 32 (1988), 212-216. MR 88j:17020
4.: E. Frenkel and N. Reshetikhin, Quantum affine algebras and deformations of the Virasoro and $\mathscr {W}$ -algebras, Comm. Math. Phys. 178 (1996), 237-264. MR 98a:17042
5.: -, The -characters of representations of quantum affine algebras and deformations of $\mathscr {W}$ -algebras, in Recent developments in quantum affine algebras and related topics (Raleigh, NC, 1998), Contemp. Math., 248, Amer. Math. Soc., Providence, RI, 1999, 163-205. MR 2002f:17022
6.: E. Frenkel and E. Mukhin, Combinatorics of -characters of finite-dimensional representations of quantum affine algebras, Comm. Math. Phys. 216 (2001), 23-57. MR 2002c:17023
7.: G. Hatayama, A. Kuniba, M. Okado, T. Takagi and Y. Yamada, Remarks on fermionic formula, in Recent developments in quantum affine algebras and related topics (Raleigh, NC, 1998), Contemp. Math. 248 (1999), 243-291. MR 2001m:81129
8.: A.N. Kirillov and N. Reshetikhin, Representation of Yangians and multiplicity of the inclusion of the irreducible components of the tensor product of representations of simple Lie algebras, J. Sov. Math. 52 (1990), 3156-3164. MR 89b:17012
9.: H. Knight, Spectra of tensor products of finite-dimensional representations of Yangians, J. Algebra 174 (1995), 187-196. MR 96g:17015
10.: A. Kuniba, T. Nakanishi and J. Suzuki, Functional relations in solvable lattice models: I. Functional relations and representation theory, Int. J. Mod. Phys. A 9 (1994), 5215-5266. MR 96h:82003
11.: A. Kuniba, T. Nakanishi and Z. Tsuboi, The canonical solutions of the -systems and the Kirillov-Reshetikhin conjecture, Comm. Math. Phys. 227 (2002), 155-190. MR 2003e:81085
12.: G. Lusztig, Ferminonic form and Betti numbers, preprint, arXiv:math.QA/0005010.
13.: H. Nakajima, Quiver varieties and finite dimensional representations of quantum affine algebras, J. Amer. Math. Soc., 14 (2001), 145-238. MR 2002i:17023
14.: -, -analogue of the -characters of finite dimensional representations of quantum affine algebras, in ``Physics and Combinatorics'', Proceedings of the Nagoya 2000 International Workshop, World Scientific, 2001, 195-218. MR 2003b:17020
15.: -, Quiver varieties and -analogs of -characters of quantum affine algebras, preprint, arXiv:math.QA/0105173.
16.: -,-analogs of -characters of quantum affine algebras of type , , to appear.
17.: M. Varagnolo and E. Vasserot, Standard modules of quantum affine algebras, in Duke Math. J. 111 (2002), 509-533. MR 2003g:17030
18.: -, Perverse sheaves and quantum Grothendieck rings, preprint, arXiv:math. QA/0103182.

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