Table of Contents Introduction 1 1. Preliminaries 4 2. The Tensor Product Realization 16 3. The Dominant Weights of ®MV{wuXr) 38 4. The Dominant Weights of V(A, Xr) 45 5. Dimensions and Polynomials 56 6. Stability of gr(®M'V(uuXr)) ® gr(®M"V(ui,Xr)) 60 7. Stability of V(\,Xr) g V(\',Xr) 71 8. Multiplicities of the Dominant Weights of V ^ A , ^ ) 82 9. Algorithms and Examples 95 Notation 154 References 161 iii
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