Finite-dimensional representations of quantum affine algebras at roots of unity
Tóm tắt
We describe explicitly the canonical map
Từ khóa
Tài liệu tham khảo
[AS] E. Abe and K. Suzuki, On normal subgroups of Chevalley groups over commutative rings, Tôhoku Math. J. 28 (1976), 185–198.
[Be1] J. Beck, Braid group action and quantum affine algebras, Comm. Math. Phys. 165 (1994), 555–568.
[Be2] \bysame, Convex bases of PBW type for quantum affine algebras, Comm. Math. Phys. 165 (1994), 193–199.
[CP2] \bysame, Quantum affine algebras and their representations, Proceedings of the Banff Conference, Canad. Math. Soc., 1994 (to appear).
[Da] I. Damiani, A basis of type Poincaré–Birkhoff–Witt for the quantum algebra of 𝔰𝔩₂, J. Algebra 161 (1993), 291–310.
[DC–K] C. De Concini C. and V. G. Kac, Representations of quantum groups at roots of 1, Progr. in Math., vol. 92, Birkhäuser, 1990, pp. 471–506.
[DC–K–P1] C. De Concini, V. G. Kac and C. Procesi, Quantum coadjoint action, J. Amer. Math. Soc. 5 (1992), 151–190.
[DC–K–P2] \bysame, Some remarkable degenerations of quantum groups, Comm. Math. Phys. 157 (1993), 405–427.
[DC–K–P3] \bysame, Some quantum analogues of solvable Lie groups, Proceedings of the International Colloquium on Geometry and Analysis (Bombay, 1992), Oxford Univ. Press, London and New York, 1995, pp. 41–66.
[DC–P] C. De Concini and C. Procesi, Quantum groups, Lecture Notes in Math., vol. 1565, Springer-Verlag, Berlin and New York, 1994.
[D1] V. G. Drinfel’d, Quantum groups, Proc. ICM Berkeley 1 (1986), 789–820.
[D2] \bysame, A new realization of Yangians and quantized affine algebras, Soviet Math. Dokl. 36 (1988), 212–216.
[G] I. Grojnowski, Representations of affine Hecke algebras (and affine quantum 𝐺𝐿_{𝑛}) at roots of unity, Internat. Math. Res. Notes 4 (1994), 215–217.
[J1] M. Jimbo, A q-difference analog of 𝑈(𝔤) and the Yang–Baxter equation, Lett. Math. Phys. 10 (1985), 63–69.
[J2] \bysame, A 𝑞-analog of 𝑈(𝑔𝑙(𝑁+1)), Hecke algebras, and the Yang–Baxter equation, Lett. Math. Phys. 11 (1986), 247–252.
[K] V. G. Kac, Infinite dimensional Lie algebras,, Third Edition, Cambridge Univ. Press, Cambridge, 1990.
[KP] V. G. Kac and D. H. Peterson, Defining relations of certain infinite–dimensional groups, Astérisque, hors série (1985), 155–208.
[LSS] S. Levendorskii, Y. Soibelman, and V. Stukopin, The quantum Weyl group and the universal quantum R-matrix for affine Lie algebras, Lett. Math. Phys. 27 (1993), 253–264.
[L1] G. Lusztig, Introduction to quantum groups, Birkhäuser, Boston and Basel, 1993.
[L2] \bysame, Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J. Amer. Math. Soc. 3 (1990), 257–296.
[Pa] P. Papi, Convex orderings in affine root systems, preprint.
[Re] N. Reshetikhin, Quasitriangularity of quantum groups at roots of 1, hep-th/9403105 preprint.
[Ro] M. Rosso, Finite dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), 581–593.
[St] R. Steinberg, Lectures on Chevalley groups, Yale University, 1967.
