Representations of quantum affinizations and fusion product

Transformation Groups

Volumn 10, Issue 2, 2005, Pages 163-200

  Hernandez, David ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

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EID: 27844489637     PISSN: 10834362     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00031-005-1005-9     Document Type: Article

References (47)

1. [AK] T. Akasaka, M. Kashiwara, Finite-dimensional representations of quantum affine algebras, Publ. Res. Inst. Math. Sci. 33, no. 5, 839-867 (1997).
2. [Be] J. Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165, no. 3, 555-568 (1994).
3. [Bo] N. Bourbaki, Groupes et algèbres de Lie, Chapitres IV-VI, Hermann, Paris, 1968.
4. [CP1] V. Chari, A. Pressley, Quantum affine algebras, Comm. Math. Phys. 142 (1991), no. 2, 261-283.
5. [CP2] V. Chari, A. Pressley, Minimal affinizations of representations of quantum groups: the simply-laced case, Lett. Math. Phys. 35 (1995), no. 2, 99-114.
6. [CP3] V. Chari, A. Pressley, Quantum affine algebras and their representations, in: Representations of Groups (Banff, AB, 1994), CMS Conf. Proc., 16 (1995), 59-78.
7. [CP4] V. Chari, A. Pressley, A Guide to Quantum Groups, Cambridge University Press, Cambridge (1994).
8. [Da] I. Damiani, La R-matrice pour les algèbres quantiques de type affine non tordu, Ann. Sci. École Norm. Sup. (4) 31 (1998), no. 4, 493-523.
9. [Dr1] V. G. Drinfel'd, Quantum groups, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), vol. 1, AMS, 1987, 798-820.
10. Engl. transl.: V. G. Drinfel'd, A new realization of Yangians and of quantum affine algebras, Soviet Math. Dokl. 36 (1988), no. 2, 212-216.
11. q(gl(n)), Comm. Math. Phys. 156 (1993), no. 2, 277-300.
12. [DI] J. Ding, K. Iohara, Generalization of Drinfeld quantum affine algebras, Lett. Math. Phys. 41 (1997), no. 2, 181-193.
13. [DJ] J. Ding, N. Jing, On a combinatorial identity, Internat. Math. Res. Notices 6 (2000), 325-332.
14. [E] B. Enriquez, On correlation functions of Drinfeld currents and shuffle algebras, Transform. Groups 5 (2000), no. 2, 111-120.
15. [EM] P. I. Etingof, A. A. Moura, Elliptic central characters and blocks of finite dimensional representations of quantum affine algebras, Represent. Theory 7 (2003), 346-373.
16. [F] J. Fuchs, Fusion rules in conformal field theory, Fortschr. Phys. 42 (1994), no. 1, 1-48.
17. [FM] E. Frenkel, E. Mukhin, Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras, Comm. Math. Phys. 216 (2001), no. 1, 23-57.
18. [FR] E. Frenkel, N. Reshetikhin, The q-characters of representations of quantum affine algebras and deformations of W-algebras, in: Recent Developments in Quantum Affine Algebras and Related Topics, Contemp. Math. 248 (1999), 163-205.
19. [Gr] P. Grosse, On quantum shuffle and quantum affine algebras, preprint (2001), arXiv: math.QA/0107176.
20. [Gu] A. Guichardet, Groupes quantiques. Introduction au point de vue formel, Savoirs Actuels, InterEditions, Paris, CNRS Editions, Paris, 1995.
21. [GKV] V. Ginzburg, M. Kapranov, E. Vasserot, Langlands reciprocity for algebraic surfaces, Math. Res. Lett. 2 (1995), no. 2, 147-160.
22. [HI] D. Hernandez, t-analogues des opérateurs d'écrantage associés aux q-caractères, Int. Math. Res. Not. 2003 (2003), no. 8, 451-475.
23. [H2] D. Hernandez, Algebraic approach to q,t-characters, Adv. Math. 187 (2004), no. 1, 1-52.
24. [H3] D. Hernandez, The t-analogs of q-characters at roots of unity for quantum affine algebras and beyond, J. Algebra 279 (2004), no. 2, 514-557.
25. [Ja] J. C. Jantzen, Lectures on Quantum Groups, Graduate Studies in Mathematics, vol. 6, AMS, Providence, RI, 1996.
26. [Jim] M. Jimbo, A q-difference analogue of U(g) and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), no. 1, 63-69.
27. [Jin] N. Jing, Quantum Kac-Moody algebras and vertex representations, Lett. Math. Phys. 44 (1998), no. 4, 261-271.
28. [Ka] V. Kac, Infinite dimensional Lie algebras, Third Edition, Cambridge University Press, Cambridge, New York, 1990.
29. [Kn] H. Knight, Spectra of tensor products of finite-dimensional representations of Yangians, J. Algebra 174 (1995), no. 1, 187-196.
30. [KT] S. M. Khoroshkin, V. N. Tolstoy, On Drinfeld's realization of quantum affine algebras, in: Infinite-Dimensional Geometry in Physics (Karpacz, 1992), J. Geom. Phys. 11 (1993), no. 1-4, 445-452.
31. [L] G. Lusztig, Introduction to Quantum Groups, Progress in Mathematics, vol. 110, Birkhäuser Boston, Inc., Boston, MA, 1993.
32. (1), Lett. Math. Phys. 27 (1993), no. 4, 253-264.
33. n+1+1, tor), (n ≥ 2), J. Math. Phys. 41 (2000), no. 10, 7079-7098.
34. 2,tor) and R matrices, J. Math. Phys. 42 (2001), no. 5, 2293-2308.
35. [N1] H. Nakajima, Quiver varieties and finite-dimensional representations of quantum affine algebras, J. Amer. Math. Soc. 14 (2001), no. 1, 145-238.
36. [N2] H. Nakajima, Quiver varieties and t-analogs of q-characters of quantum affine algebras, Ann. Math. 160 (2004), 1057-1097.
37. [N3] H. Nakajima, Geometric construction of representations of affine algebras, Proceedings of the International Congress of Mathematicians (Beijing, 2002), vol. I, Higher Ed. Press, Beijing, 2002, 423-438.
38. [R] M. Rosso, Représentations des groupes quantiques, Séminaire Bourbaki, exp. no. 744, Astérisque 201-203 (1992), 443-483.
39. [Sa] Y. Saito, Quantum toroidal algebras and their vertex representations, Publ. Res. Inst. Math. Sci. 34 (1998), no. 2, 155-177.
40. [Sc] O. Schiffmann, Noncommutative protective curves and quantum loop algebras, Duke Math. J., 121 (2004), no. 1, 113-168.
41. n), Transform. Groups 3 (1998), no. 1, 75-102.
42. N, Publ. Res. Inst. Math. Sci. 35 (1999), no. 3, 407-450.
43. [VV1] M. Varagnolo, E. Vasserot, Double-loop algebras and the Fock space, Invent. Math. 133 (1998), no. 1, 133-159.
44. [VV2] M. Varagnolo, E. Vasserot, Standard modules of quantum affine algebras, Duke Math. J. 111 (2002), no. 3, 509-533.