Monomials of q and q, t-characters for non simply-laced quantum affinizations

Mathematische Zeitschrift

Volumn 250, Issue 2, 2005, Pages 443-473

  Hernandez, David ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18244389676     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-005-0762-4     Document Type: Article

References (27)

1. Akasaka et, T., Kashiwara, M.: Finite-dimensional representations of quantum affine algebras. Publ. Res. Inst. Math. Sci. 33(5), 839-867 (1997)
2. Beck, J.: Braid group action and quantum affine algebras. Comm. Math. Phys. 165(3), 555-568 (1994)
3. Bourbaki, N.: Groupes et algèbres de Lie, Chapitres IV-VI, Hermann (1968)
4. Chari, V., Pressley, A.: Quantum affine algebras and their representations, in Representations of groups (Banff, AB, 1994), 59-78, CMS Conf. Proc, 16, Amer. Math. Soc., Providence, RI (1995)
5. Chari, V., Pressley, A.: A Guide to Quantum Groups. Cambridge University Press, Cambridge, 1994
6. Chari, V., Pressley, A.: Weyl modules for classical and quantum affine algebras, Represent. Theory 5, 191-223 (electronic) (2001)
7. 2, Quantum groups and Lie theory (Durham, 1999), 48-62, London Math. Soc. Lecture Note Ser., 290, Cambridge Univ. Press, Cambridge 2001
8. Drinfel'd, V.G.: Quantum groups, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), 798-820, Amer. Math. Soc., Providence, RI, (1987)
9. Drinfel'd, V.G.: A new realization of Yangians and of quantum affine algebras. Soviet Math. Dokl. 36(2), 212-216 (1988)
10. Frenkel, E., Mukhin, E.: Combinatorics of q-Characters of Finite-Dimensional Representations of Quantum Affine Algebras. Comm. Math. Phy. 216(1), 23-57 (2001)
11. Frenkel, E., Reshetikhin, N.: Quantum affine algebras and deformations of the Virasoro and W-algebras. Comm. Math. Phys. 178(1), 237-264 (1996)
12. Frenkel, E., Reshetikhin, N.: Deformations of W-algebras associated to simple Lie algebras. Comm. Math. Phys. 197(1), 1-32 (1998)
13. Frenkel, E., Reshetikhin, N.: The q-Characters of Representations of Quantum Affine Algebras and Deformations of W-Algebras, Recent Developments in Quantum Affine Algebras and related topics. Cont. Math. 248, 163-205 (1999)
14. Hernandez, D.: t-analogues des opérateurs d'écrantage associés aux q-caractères. Int. Math. Res. Not. 2003(8), 451-475 (2003)
15. Hernandez, D.: Algebraic Approach to q,t-Characters. Adv. Math. 187(1), 1-52 (2004)
16. Hernandez, D.: The t-analogs of q-characters at roots of unity for quantum affine algebras and beyond. J. Algebra 279(2), 514-557 (2004)
17. Hernandez, D.: Representations of Quantum Affinizations and Fusion Product, to appear in Transform. Groups (preprint arXiv:math.QA/0312336)
18. Jimbo, M.: A q-difference analogue of u(g) and the Yang-Baxter equation. Lett. Math. Phys. 10(1), 63-69 (1985)
19. Jing, N.: Quantum Kac-Moody algebras and vertex representations. Lett. Math. Phys. 44(4), 261-271 (1998)
20. Knight, H.: Spectra of tensor products of finite-dimensional representations of Yangians. J. Algebra 174(1), 187-196 (1995)
21. n+1,tor)(n ≥ 2). J. Math. Phys. 41(10), 7079-7098 (2000)
22. Nakajima, H.: Quiver varieties and finite-dimensional representations of quantum affine algebras. J. Amer. Math. Soc. 14(1), 145-238 (2001)
23. Nakajima, H.: t-Analogue of the q-Characters of Finite Dimensional Representations of Quantum Affine Algebras, "Physics and Combinatorics", Proc. Nagoya 2000 International Workshop, World Scientific, pp 181-212 (2001)
24. Nakajima, H.: Quiver Varieties and t-Analogs of q-Characters of Quantum Affine Algebras. To appear in Ann. of Math, (preprint arXiv:math.QA/0105173)
25. n, in Combinatorial and geometric representation theory (Seoul, 2001), 141-160, Contemp. Math. 325, Amer. Math. Soc. Providence, RI (2003)
26. Nakajima, H.: Geometric construction of representations of affine algebras. In: Proceedings of the International Congress of Mathematicians, Volume I, 2003, pp 423-438
27. Varagnolo, M., Vasserot, E.: Standard modules of quantum affine algebras. Duke Math. J. 111(3), 509-533 (2002)