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Thus the 4 components of our partial quiver P = − LLRRRLRR give the 4 rectangles shown in Figure 11. We now observe that for a component of type L immediately followed by a component of type R the two corresponding rectangles fit together from the left hand corner. Also, for a component of type R immediately followed by a component of type L the two rectangles fit together from the right hand corner. This can be observed in the four rectangles above, in which the first and the second fit from the left, the second and the third from the right, and the third and the fourth from the left.

Math. , 3:447–498, 1990. [5] G. Lusztig. Introduction to quantized enveloping algebras. Progr. , 105:49–95, 1992. [6] G. Lusztig. Introduction to Quantum Groups. Birkh¨auser, Boston, 1993. [7] R. J. Marsh. More tight monomials in quantized enveloping algebras. J. , 204:711–732, 1998. [8] R. J. Marsh. Rectangle diagrams for the Lusztig cones of quantized enveloping algebras of type A. Preprint, 1998. [9] A. Premat. The Lusztig cone and the image of the Kashiwara map. Private communication, 1999.

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