Special Bases of Irreducible Modules of the Quantized Universal Enveloping Algebra Uv(gl(n)) Original Research Article

In this paper we construct a basis for an irreducible module of the quantized enveloping algebra Uv (gl(n)) which is a q-analogue of the special basis of an irreducible GL(n)-module introduced by C. de Concini and D. Kazhdan (Israel J. Math.40, 1980, 275-290). We conjecture the basis is the dual basis of the canonical basis introduced by G. Lusztig (J. Amer. Math. Soc.3, 1990, 447-498).