Special bases of irreducible modules of the quantized universal enveloping algebra \(U_ v(gl(n))\) (Q1209826)

The author constructs a basis for an irreducible module of the quantized enveloping algebra \(U_ v(gl(n))\) which is a \(q\)-analogue of the special basis of an irreducible \(GL(n)\)-module introduced by \textit{C. de Concini} and \textit{D. Kazhdan} [Isr. J. Math. 40, 275-290 (1981; Zbl 0537.20006)]. Also, he conjectures the basis is the dual basis of the canonical basis introduced by \textit{G. Lusztig} [J. Am. Math. Soc. 3, 447-498 (1990; Zbl 0703.17008)].