The restricted Kirillov-Reshetikhin modules for the current and twisted current algebras

Communications in Mathematical Physics

Volumn 266, Issue 2, 2006, Pages 431-454

  Chari, Vyjayanthi ^a   Moura, Adriano ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF CAMPINAS   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746215051     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0032-2     Document Type: Article

References (19)

1. Bourbaki, N.: Groupes et algèbras de Lie. Chapitres 4,5,6, Paris: Hermann, (1968)
2. Chart, V.: On the fermionic formula and the Kirillov-Reshetikhin conjecture. Int. Math. Res. Not. 12, 629-654 (2001)
3. r+1. http://arxiv.org/list/math.QA/0502165, 2005
4. Chari, V., Pressley, A.: Weyl modules for classical and quantum affine algebras. Represent. Theory 5, 191-223 (2001)
5. Feigin, B., Loktev S.: On Generalized Kostka Polynomials and the Quantum Verlinde Rule. In: Differential topology, infinite-dimensional Lie algebras, and applications, Amer. Math. Soc. Transl. Ser. 2, Vol. 194, Providence, RI:/Amer.Math.Soc., 1999, pp. 61-79,
6. Feigin, B., Loktev, S., Kirillov, A.N.: Combinatorics and Geometry of Higher Level Weyl Modules. http://arxiv.org/list/math.QA/0503315, 2005
7. Fourier, G., Littelmann, P.: Tensor product structure of affine Demazure modules and limit constructions. http://arxiv.org/list/math.RT/0412432, 2004
8. Fulton W., Harris, J.: Representation Theory - A first course. GTM bf 129, Berlin-Heidelberg-New York: Springer-Verlag. 1991
9. Hatayama, G., Kuniba, A., Okado, M., Takagi, T., Yamada, Y.: Remarks on the Fermionic Formula. Contemp. Math. 248, 243-291 (1999)
10. Hatayama, G., Kuniba, A., Okado, M., Takagi, T., Tsuboi, Z.: Paths, Crystals and Fermionic Formulae, Prog. Math. Phys. 23, 205-272 (2002)
11. Humphreys, J.: Introduction to Lie Algebras and Representation Theory. GTM 9, Berlin-Heidelberg-New York: Springer-Verlag, 1972
12. Kac, V.: Infinite dimensional Lie algebras. Cambridge: Cambridge Univ. Press, 1985
13. Kirillov, A.N., Reshetikhin, N.: Representations of Yangians and multiplicities of ocurrence of the irreducible components of the tensor product of simplie Lie algebras. J. Sov. Math. 52, no. 5, 393-403 (1981)
14. Kleber, M.: Combinatorial structure of finite-dimensional representations of Yangians: the simply-laced case. Int. Math. Res. Not. 7, no. 4, 187-201 (1997)
15. Naito, S., Sagaki, D.: Path Model for a Level Zero Extremal Weight Module over a Quantum Affine Algebra. http://arxiv.org/list/math.QA/0210450, 2002
16. Naito, S., Sagaki, D.: Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras. http://arxiv.org/list/math.QA/0503287, 2005
17. (1). http://arxiv.org/list/math.QA/0408113, 2004, to appear in J. Alg. Combin.
18. Parthasarathy, K., Rao, R., Varadarajan, V.: Representations of complex semi-simple Lie groups and Lie Algebras. Ann. Math. 85, 38-429 (1967)
19. Varadarajan, V.: Lie Groups, Lie Algebras, and Their Representations. GTM 102, Berlin-Heidelberg-New York: Springer-Verlag, 1974