Hecke symmetries

Journal of Pure and Applied Algebra

Volumn 152, Issue 1-3, 2000, Pages 109-121

  Hài, Phùng Hồ ^a  

^a INSTITUTE OF MATHEMATICS   (Viet Nam)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034664303     PISSN: 00224049     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-4049(99)00145-0     Document Type: Article

References (24)

1. [1] E. Cremmer, J.-L. Gervais, The quantum groups structure associated with non-linearly extended Virasoro algebras, Comm. Math. Phys. 134 (1990) 619-632.
2. [2] R. Dipper, G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc. 52 (3) (1986) 20-52.
3. [3] A. Edrei, Proof of a conjecture of Schoenberg on the generating function of a totally positive sequence, Canad. J. Math. 5 (1953) 86-94.
4. [4] L.D. Faddeev, P.N. Pyatov, The differential calculus on quantum linear groups, in: R.L. Dobrushin et al. (Eds.), Contemporary Mathematical Physics. F.A. Berezin Memorial Volume, Vol. 175(31) of Transl., Ser. 2, American Mathematical Society, Providence, RI, 1996, pp. 35-47.
5. [5] D.I. Gurevich, Algebraic aspects of the quantum Yang - Baxter equation, Leningrad Math. J. 2 (4) (1991) 801-828.
6. [6] T.J. Hodges, On the Cremmer - Grevais quantizations of SL(n), Int. Math. Res. Not. 10 (1995) 465-481.
7. [7] A.P. Isaev, P.N. Pyatov, Covariant differential complexes on quantum linear groups, J. Phys. A, Math. Gen. 28 (8) (1995) 2227-2246.
8. [8] M. Jimbo, A q-analogue of U(gl(N + 1)), Hecke algebra, and the Yang - Baxter equation, Lett. Math. Phys. 11 (1986) 247-252.
9. [9] R. Larson, J. Towber, Two dual classes of bialgebras related to the concepts of quantum groups and quantum lie algebra, Commun. Algebra 19 (12) (1991) 3295-3345.
10. [10] V.V. Lyubashenko, Hopf algebras and vector symmetries, Russian Math. Survey 41 (5) (1986) 153-154.
11. [11] V.V. Lyubashenko, Superanalysis and solutions to the triangles equation, Ph.D. Thesis, Kiev, 1987.
12. [12] V.V. Lyubashenko, A. Sudbery, Quantum super groups of GL(n|m) type: differential forms, Koszul complexes and Berezinians, Duke Math. J. 90 (1997) 1-62.
13. [13] I.G. Macdonald, Symmetric Functions and the Hall Polynomials, 2nd ed., Oxford University Press, Oxford, 1979.
14. [14] S. Majid, M. Markl, Glueing operation for R-matrices, quantum groups and link-invariants of Hecke type, Math. Proc. Camb. Philos. Soc. 119 (1) (1996) 139-166.
15. [15] Yu.I. Manin, Gauge Field Theory and Complex Geometry, Springer, Berlin, 1988.
16. [16] Yu.I. Manin, Multiparametric quantum deformation of the general linear supergroups, Comm. Math. Phys. 123 (1989) 163-175.
17. n, J. Algebra 192 (2) (1997) 734-748.
18. n, Preprint ICTP/97101, q-alg/9708007, 1997.
19. q(m\n), J. Algebra 211 (1999) 363-383. Available at xxx.lanl.gov/dvi/q-alg/9511023.
20. [20] Phung Ho Ha′i, Poincaré series of quantum spaces associated to Hecke operators, Acta Math. Vietnam 24 (2) (1999) 235-246. Available at xxx.lanl.gov/dvi/q-alg/9711020.
21. [21] N. Reshetikhin, V. Turaev, Ribbon graph and their invariant derived from quantum groups, Comm. Math. Phys. 127 (1990) 1-26.
22. [22] P. Schauenburg, On Coquasitriangular Hopf Algebras and the Quantum Yang-Baxter Equation, Algebra Berichte 67, Verlag Reinhard Fischer, Munich, 1992.
23. [23] M. Takeuchi, D. Tambara, A new one-parameter family of 2 × 2 quantum matrices, Hokkaido Math. J. XXI (3) (1992) 409-419.
24. [24] M. Takeuchi, D. Tambara, Proc. Japan Acad. 67 (8) (1991) 267-269.