Paths and tableaux descriptions of Jacobi-Trudi determinant associated with quantum affine algebra of type D n

Journal of Algebraic Combinatorics

Volumn 26, Issue 2, 2007, Pages 253-290

  Nakai, Wakako ^a   Nakanishi, Tomoki ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

Lattice path; Q character; Quantum group; Young tableau

Indexed keywords

ALGEBRA; QUANTUM THEORY; SET THEORY;

LATTICE PATH; Q-CHARACTER; QUANTUM GROUP; YOUNG TABLEAU;

JACOBIAN MATRICES;

EID: 34548090446     PISSN: 09259899     EISSN: 15729192     Source Type: Journal    
DOI: 10.1007/s10801-007-0057-4     Document Type: Article

References (21)

1. Bazhanov, V.V., Reshetikhin, N.: Restricted solid-on-solid models connected with simply laced algebras and conformal field theory. J. Phys. A 23, 1477-1492 (1990)
2. Chari, V., Moura, A.: Characters of fundamental representations of quantum affine algebras. Acta Appl. Math. 90, 43-63 (2006)
3. Chari, V., Pressley, A.: Quantum affine algebras. Commun. Math. Phys. 142, 261-283 (1991)
4. Drinfel'd, V.: Hopf algebras and the quantum Yang-Baxter equation. Soviet. Math. Dokl. 32, 254-258 (1985)
5. Drinfel'd, V.: A new realization of Yangians and quantized affine algebras. Soviet. Math. Dokl. 36, 212-216 (1988)
6. Frenkel, E., Mukhin, E.: Combinatorics of q-characters of finite-dimensional representations of quantum affine algebras. Commun. Math. Phys. 216, 23-57 (2001)
7. Frenkel, E., Reshetikhin, N.: The q-characters of representations of quantum affine algebras and deformations of W-algebras. Contemp. Math. 248, 163-205 (1999)
8. Fulmek, M., Krattenthaler, C.: Lattice path proofs for determinantal formulas for symplectic and orthogonal characters. J. Combin. Theory Ser. A 77, 3-50 (1997)
9. Gessel, I., Viennot, G.: Binomial determinants, paths, and hook length formulae. Adv. Math. 58, 300-321 (1985)
10. Hernandez, D.: The Kirillov-Reshetikhin conjecture and solutions of T-systems. J. Reine Angew. Math. 596, 63-87 (2006)
11. Jimbo, M.: A q-difference analogue of U(ǧ) and the Yang-Baxter equation. Lett. Math. Phys. 10, 63-69 (1985)
12. Kashiwara, M., Nakashima, T.: Crystal graphs for representations of the q-analogue of classical Lie algebras. J. Algebra 165, 295-345 (1994)
13. n. J. Algebra 107, 466-511 (1987)
14. (1) ) from the analytic Bethe ansatz. J. Phys. A 28, 6211-6226 (1995)
15. Kuniba, A., Suzuki, J.: Analytic Bethe ansatz for fundamental representations of Yangians. Commun. Math. Phys. 173, 225-264 (1995)
16. Macdonald, I.G.: Symmetric Functions and Hall Polynomials, 2nd edn. Oxford University Press, New York (1995)
17. n case. J. Phys. A: Math. Gen. 39, 2083-2115 (2006)
18. n. Preprint, math.QA/0604158
19. n. Contemp. Math. 325, 141-160 (2003)
20. (1). Represent. Theory 7, 101-163 (2003)
21. (1). J. Algebr. Comb. 23, 317-354 (2006)