Martin W. Liebeck, Imperial College, London, United Kingdom.Gary M. Seitz, University of Oregon, Eugene, Oregon.Donna M. Testerman, Ecole Polytechnique Federale de Lausanne, Switzerland.

• 1. Introduction2. Notation3. Level set-up4. Results from the Literature5. Composition Factors In Levels6. Multiplicity-free families7. Initial Lemmas8. The case $X = A_2$9. The case $\delta = r\omega _k$ with $r,k\ge 2$10. The case $\delta = r\omega _1$, $r\ge 2$11. The case $\delta = \omega _i$ with $i\ge 3$12. The case $\delta = \omega _2$13. The case $\delta = \omega _1+\omega _{l+1}$14. Proof of Theorem , Part I: $V_{C^i}(\mu ^i)$ is usually trivial15. Proof of Theorem , Part II: $\mu ^0$ is not inner16. Proof of Theorem , Part III: $\langle \lambda , \gamma \rangle = 0$17. Proof of Theorem , Part IV: Completion

Martin W. Liebeck, Imperial College, London, United Kingdom.Gary M. Seitz, University of Oregon, Eugene, Oregon.Donna M. Testerman, Ecole Polytechnique Federale de Lausanne, Switzerland.

• 1. Introduction2. Notation3. Level set-up4. Results from the Literature5. Composition Factors In Levels6. Multiplicity-free families7. Initial Lemmas8. The case $X = A_2$9. The case $\delta = r\omega _k$ with $r,k\ge 2$10. The case $\delta = r\omega _1$, $r\ge 2$11. The case $\delta = \omega _i$ with $i\ge 3$12. The case $\delta = \omega _2$13. The case $\delta = \omega _1+\omega _{l+1}$14. Proof of Theorem , Part I: $V_{C^i}(\mu ^i)$ is usually trivial15. Proof of Theorem , Part II: $\mu ^0$ is not inner16. Proof of Theorem , Part III: $\langle \lambda , \gamma \rangle = 0$17. Proof of Theorem , Part IV: Completion

Martin W. Liebeck, Imperial College, London, United Kingdom.Gary M. Seitz, University of Oregon, Eugene, Oregon.Donna M. Testerman, Ecole Polytechnique Federale de Lausanne, Switzerland.

• 1. Introduction2. Notation3. Level set-up4. Results from the Literature5. Composition Factors In Levels6. Multiplicity-free families7. Initial Lemmas8. The case $X = A_2$9. The case $\delta = r\omega _k$ with $r,k\ge 2$10. The case $\delta = r\omega _1$, $r\ge 2$11. The case $\delta = \omega _i$ with $i\ge 3$12. The case $\delta = \omega _2$13. The case $\delta = \omega _1+\omega _{l+1}$14. Proof of Theorem , Part I: $V_{C^i}(\mu ^i)$ is usually trivial15. Proof of Theorem , Part II: $\mu ^0$ is not inner16. Proof of Theorem , Part III: $\langle \lambda , \gamma \rangle = 0$17. Proof of Theorem , Part IV: Completion