Capillary Gravity Water Waves Linearized at Monotone Shear Flows

Xiao Liu, University of Illinois, Champaign, Illinois. Chongchun Zeng, Georgia Institute of Technology, Atlanta, Georgia

• Chapters; Introduction; 1. Setting and General Methods; 1. Finite groups of Lie type; 2. Hecke algebras; 2. Decomposition Matrices; 3. Description of the strategy; 4. Decomposition matrices at $d_\ell (q)=2$; 5. Decomposition matrices at $d_\ell (q)=3$; 6. Decomposition matrices at $d_\ell (q)=6$; 7. Decomposition matrices at $d_\ell (q)=5,7,8,10,12,14$; 8. On a conjecture of Craven