A Chevalley-Kostant presentation of basic modules for sl(2) and the associated affine KPRV determinants at q = 1

Bulletin des Sciences Mathematiques

Volumn 125, Issue 2, 2001, Pages 85-108

  Greenstein, Jacob ^a   Joseph, Anthony ^a,b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b INSTITUT DE MATHÉMATIQUES DE JUSSIEU   (France)

Author keywords

Affine lie algebras; Integrable modules; KPRV determinants; Quantum affine algebras

Indexed keywords

EID: 0035256057     PISSN: 00074497     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0007-4497(00)01077-0     Document Type: Article

References (15)

1. Andrews G.E., The Theory of Partitions, Cambridge Univ. Press, Cambridge, 1998.
2. Chari V., Pressley A., Quantum affine algebras, Comm. Math. Phys. 142 (2) (1991) 261-283.
3. De Concini C., Kac V.G., Representations of quantum groups at roots of 1, in: Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory (Paris, 1989), Birkhäuser, Boston MA, 1990, pp. 471-506.
4. Drinfel'd V.G., On some unsolved problems in quantum group theory, in: Quantum Groups (Leningrad, 1990), Springer, Berlin, 1992, pp. 1-8.
5. Greenstein J., Characters of Simple Bounded Modules Over an Untwisted Affine Algebra, Preprint, Weizmann, 1999.
6. Greenstein J., Characters of bounded sl(2) modules, J. Algebra 230 (2) (2000) 540-557.
7. Joseph A., A completion of the quantized enveloping algebra of a Kac - Moody algebra, J. Algebra 214 (1) (1999) 235-275.
8. Joseph A., On an affine quantum KPRV determinant at q = 1, Bull. Sci. Math. 125 (1) (2001) 1-26.
9. Joseph A., Letzter G., Evaluation of the Quantum Affine PRV Determinant, Preprint, Weizmann, 2000.
10. Joseph A., Todorić D., On the Quantum KPRV Determinants for Semisimple and Affine Lie Algebras, Preprint, Weizmann, 1999.
11. Kac V.G., Infinite Dimensional Lie Algebras, Cambridge Univ. Press, Cambridge, 1992.
12. Kostant B., Lie group representations on polynomial rings, Amer. J. Math. 85 (1963) 327-404.
13. Kostant B., Clifford algebra analogue of the Hopf - Koszul - Samelson theorem, the ρ-decomposition C (g) = end V ρ ⊕ C (P), and the g-module structure of ∧ g, Adv. Math. 125 (2) (1997) 275-350.
14. Lang S., Algebra, Addison-Wesley, Reading, MA, 1965.
15. Parthasarathy K.R., Ranga Rao R., Varadarajan V.S., Representations of complex semi-simple lie groups and lie algebras, Ann. of Math. 85 (1967) 383-429.