Demazure modules and vertex models: The sl(2) case

Journal of Mathematical Physics

Volumn 39, Issue 3, 1998, Pages 1601-1622

  Foda, Omar ^a,d   Misra, Kailash C ^b   Okado, Masato ^c  

^a UTRECHT UNIVERSITY   (Netherlands)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

^c OSAKA UNIVERSITY   (Japan)

^d UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032351580     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532402     Document Type: Article

References (23)

1. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).
2. M. Jimbo and T. Miwa, Algebraic Analysis of Solvable Lattice Models, CBMS Regional Conference Series in Mathematics, Vol. 85 (American Mathematical Society, Providence, RI, 1994).
3. S. Dasmahapatra, R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer, "Quasi-particles, conformal field theory, and q-series," in Yang Baxter Equations in Paris, edited by J.-M. Maillard (World Scientific, Singapore, 1992).
4. S. Kumar, "Demazure character formula in arbitrary Kac-Moody setting," Invent. Math. 89, 395-423 (1987).
5. O. Mathieu, "Formula de Demazure-Weyl et généralisation du théoème de Borel-Weil-Bott," C. R. Acad. Sci. Paris, Sér. I, 303, 391-394 (1986).
6. Y. B. Sanderson, "On characters of Demazure modules," Ph.D. thesis, Rutgers University, 1995.
7. P. Littelmann, "A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras," Invent. Math. 116, 329-346 (1994).
8. M. Kashiwara, "Crystalizing the q-analogue of universal enveloping algebra," Commun. Math. Phys. 133, 249-260 (1990).
9. T. Nakashima, "Crystal base and a generalization of the Littlewood-Richardson rule for the classical Lie algebras," Commun. Math. Phys. 154, 215-243 (1993).
10. M. Kashiwara, "The crystal base and Littelmann's refined Demazure character formula," Duke Math. J. 71, 839-858 (1993).
11. S-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki, "Affine crystals and vertex models," Int. J. Mod. Phys. A 7, 449-484 (1992).
12. S-J. Kang, M. Kashiwara, K. C. Misra, T. Miwa, T. Nakashima, and A. Nakayashiki, "Perfect crystals of quantum affine Lie algebras," Duke Math. J. 68, 499-607 (1992).
13. q(Ŝl(n))," Commun. Math. Phys. 134, 79-88 (1990).
14. q(ŝl(n)) at q = 0," Commun. Math. Phys. 136, 543-566 (1991).
15. E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, "Exactly solvable SOS models II: Proof of the star-triangle relation and combinatorial identities," Adv. Stud. Pure Math. 16, 17-122 (1988).
16. E. Date, M. Jimbo, A. Kuniba, T. Miwa, and M. Okado, "One dimensional configuration sums in vertex models and affine Lie algebra characters," Lett. Math. Phys. 17, 69-77 (1989).
17. M + N conformal coset models," Nucl. Phys. B 467, 247-271 (1996).
18. V. G. Kac, Infinite Dimensional Lie Algebras (Cambridge University Press, Cambridge, 1990).
19. M. Kashiwara, "On crystal bases of the q-analogue of universal enveloping algebras," Duke Math. J. 63, 465-516 (1991).
20. S-J. Kang, M. Kashiwara, and K. C. Misra, "Crystal bases of Verma modules for quantum affine Lie algebras," Compos. Math. 92, 299-325 (1994).
21. G. E. Andrews, The Theory of Partition (Addison-Wesley, Reading, MA, 1976).
22. A. Kuniba, T. Nakanishi, and J. Suzuki, "Characters in conformal field theories from thermodynamic Bethe Ansatz," Mod. Phys. Lett. A 8, 1649-1659 (1993).
23. G. Georgiev, "Combinatorial constructions of modules for infinite-dimensional Lie algebras, II. Parafermionic space," preprint, Rutgers University, q-alg/9504024.