A. A. Beilinson, G. Lusztig, and R. Macpherson, A geometric setting for the quantum deformation of GL n , Duke Math, J, pp.61-655, 1990.

N. Bourbaki, Groupes et algèbres de Lie, 1981.

R. Dipper and G. James, The q-Schur algebra, Proc. Lond, pp.23-50, 1989.

R. Dipper and G. James, q-tensor space and q-Weyl modules, Trans. Amer. Math. Soc, vol.327, pp.251-282, 1991.
DOI : 10.2307/2001842

J. Dixmier, Enveloping algebras, Graduate studies in mathematics, vol.11, 1996.

J. Du, B. Parshall, and L. Scott, Quantum Weyl Reciprocity and Tilting Modules, Communications in Mathematical Physics, vol.195, issue.2, pp.321-352, 1998.
DOI : 10.1007/s002200050392
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.134.1824

J. Du, A note on quantized Weyl reciprocity at roots of unity, Algebra Colloq, pp.363-372, 1995.

I. Grojnowski and G. Lusztig, On bases of irreducible representations of quantum GL n , in: " Kazhdan?Lusztig theory and related topics, Contemporary Mathematics 139, pp.167-174, 1989.

J. A. Green, Combinatorics and the Schur algebra, Journal of Pure and Applied Algebra, vol.88, issue.1-3, pp.89-106, 1993.
DOI : 10.1016/0022-4049(93)90015-L

R. M. Green, A straightening formula for quantized codete11minants, Communications in Algebra, vol.88, issue.9, pp.2887-2913, 1996.
DOI : 10.1080/00927879608825720

F. D. Grosshans, G. Rota, and J. A. Stein, Invariant theory and superalgebras, CBMS Regional Conference Series in Mathematics, vol.69, 1987.
DOI : 10.1090/cbms/069

. Howetel-aviv, Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond The Schur lectures, Israel Mathematical Conference Proceedings, pp.1-182, 1992.

R. Q. Huang and J. J. Zhang, Standard Basis Theorem for Quantum Linear Groups, Advances in Mathematics, vol.102, issue.2, pp.202-229, 1993.
DOI : 10.1006/aima.1993.1065

N. Jacobson, Basic algebra II " , second edition (Freeman and company, 1989.

M. Jimbo, A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation, Letters in Mathematical Physics, vol.40, issue.3, pp.247-252, 1986.
DOI : 10.1007/BF00400222

A. Joseph and G. Letzter, Local finiteness of the adjoint action for quantized enveloping algebras, Journal of Algebra, vol.153, issue.2, pp.289-318, 1992.
DOI : 10.1016/0021-8693(92)90157-H

S. Kato, Hecke algebras and quantum general linear groups, Journal of Mathematics of Kyoto University, vol.37, issue.2, pp.241-249, 1997.
DOI : 10.1215/kjm/1250518333

S. Z. Levendorskii and Y. S. Soibelman, Some applications of the quantum Weyl groups, Journal of Geometry and Physics, vol.7, issue.2, pp.241-254, 1990.
DOI : 10.1016/0393-0440(90)90013-S

B. Leclerc and J. Thibon, The Robinson?Schensted correspondence, crystal bases, and the quantum straightening at q = 0, Electron, J. Comb, vol.3, issue.3, 1996.

G. Lusztig, On quantum groups, Journal of Algebra, vol.131, issue.2, pp.466-475, 1990.
DOI : 10.1016/0021-8693(90)90187-S

G. Lusztig, Introduction to quantum groups, Progress in Mathematics, vol.110, 1993.
DOI : 10.1007/978-0-8176-4717-9

B. Parshall and J. Wang, Quantum linear groups, Memoirs of the American Mathematical Society, vol.89, issue.439, 1991.
DOI : 10.1090/memo/0439

J. Tits, Normalisateurs de tores I. Groupes de coxeter ??tendus, Journal of Algebra, vol.4, issue.1, pp.96-116, 1966.
DOI : 10.1016/0021-8693(66)90053-6