Labels of unipotent almost characters: 1: [ [ 1, 2, 3 ], [ 0, 1 ] ] 2: [ [ 1, 2 ], [ 1 ] ] 3: [ [ 0, 1, 3 ], [ 1, 2 ] ] 4: [ [ 0, 1, 2, 3 ], [ 1, 2, 3 ] ] 5: [ [ 1, 3 ], [ 0 ] ] 6: [ [ 0, 2 ], [ 2 ] ] 7: [ [ 0, 3 ], [ 1 ] ] 8: [ [ 0, 1, 2 ], [ 1, 3 ] ] 9: [ [ 3 ], [ ] ] 10: [ [ 0, 1 ], [ 3 ] ] 11: [ [ 0, 1, 3 ], [ ] ] 12: [ [ 0, 1, 2, 3 ], [ 1 ] ] In row "i,j,k:" we give the scalar product of the tensor product of almost characters i and j with almost character k, if this is nonzero and i >= j. 1, 1, 1: q^3+q+1 1, 1, 2: q^2+2 1, 1, 3: -q^2+3*q# NEGATIVE COEFF 1, 1, 4: -q^3# NEGATIVE COEFF 1, 1, 5: q+2 1, 1, 7: 4 1, 1, 8: -q# NEGATIVE COEFF 1, 1, 9: 1 2, 1, 1: q^2+2 2, 1, 2: q+2 2, 1, 3: 5 2, 1, 4: -q^2+3*q# NEGATIVE COEFF 2, 1, 5: 2 2, 1, 6: 1 2, 1, 7: 2 2, 2, 1: q+2 2, 2, 2: q+8 2, 2, 3: 2*q+6 2, 2, 4: 2*q^2+8 2, 2, 5: 3 2, 2, 6: 4 2, 2, 7: 3 2, 2, 8: 5 2, 2, 9: 1 3, 1, 1: -q^2+3*q# NEGATIVE COEFF 3, 1, 2: 5 3, 1, 3: 3*q+3 3, 1, 4: 3*q^2+4 3, 1, 6: 2 3, 1, 7: 1 3, 1, 8: 4 3, 2, 1: 5 3, 2, 2: 2*q+6 3, 2, 3: 2*q^2+2*q+12 3, 2, 4: 2*q^3+7*q+6 3, 2, 5: 2 3, 2, 6: 5 3, 2, 7: 3 3, 2, 8: 2*q+7 3, 2, 10: 1 3, 3, 1: 3*q+3 3, 3, 2: 2*q^2+2*q+12 3, 3, 3: 2*q^3+q^2+8*q+9 3, 3, 4: 2*q^4+6*q^2+2*q+10 3, 3, 5: 4 3, 3, 6: 2*q+7 3, 3, 7: q+5 3, 3, 8: 2*q^2+2*q+8 3, 3, 9: 1 3, 3, 10: 1 4, 1, 1: -q^3# NEGATIVE COEFF 4, 1, 2: -q^2+3*q# NEGATIVE COEFF 4, 1, 3: 3*q^2+4 4, 1, 4: 3*q^3+3*q+2 4, 1, 5: -q# NEGATIVE COEFF 4, 1, 6: 4 4, 1, 8: 3*q+3 4, 1, 10: 1 4, 2, 1: -q^2+3*q# NEGATIVE COEFF 4, 2, 2: 2*q^2+8 4, 2, 3: 2*q^3+7*q+6 4, 2, 4: 2*q^4+5*q^2+q+7 4, 2, 6: 2*q+5 4, 2, 7: 3 4, 2, 8: 2*q^2+q+8 4, 2, 10: 1 4, 3, 1: 3*q^2+4 4, 3, 2: 2*q^3+7*q+6 4, 3, 3: 2*q^4+6*q^2+2*q+10 4, 3, 4: 2*q^5+4*q^3+7*q+3 4, 3, 5: 4 4, 3, 6: 2*q^2+q+6 4, 3, 7: 2*q+3 4, 3, 8: 2*q^3+q^2+4*q+4 4, 3, 10: 1 4, 4, 1: 3*q^3+3*q+2 4, 4, 2: 2*q^4+5*q^2+q+7 4, 4, 3: 2*q^5+4*q^3+7*q+3 4, 4, 4: 2*q^6+2*q^4-q^3+4*q^2+3# NEGATIVE COEFF 4, 4, 5: 3*q+3 4, 4, 6: 2*q^3+4*q+3 4, 4, 7: 2*q^2+q+5 4, 4, 8: 2*q^4+4*q^2-q+5# NEGATIVE COEFF 4, 4, 9: 1 4, 4, 10: 2 5, 1, 1: q+2 5, 1, 2: 2 5, 1, 4: -q# NEGATIVE COEFF 5, 1, 5: 2 5, 1, 7: 1 5, 2, 1: 2 5, 2, 2: 3 5, 2, 3: 2 5, 2, 5: 1 5, 2, 6: 1 5, 2, 7: 1 5, 3, 2: 2 5, 3, 3: 4 5, 3, 4: 4 5, 3, 6: 1 5, 3, 7: 1 5, 3, 8: 1 5, 4, 1: -q# NEGATIVE COEFF 5, 4, 3: 4 5, 4, 4: 3*q+3 5, 4, 6: 1 5, 4, 8: 3 5, 5, 1: 2 5, 5, 2: 1 5, 5, 5: 2 5, 5, 7: 1 5, 5, 9: 1 6, 1, 2: 1 6, 1, 3: 2 6, 1, 4: 4 6, 1, 8: 1 6, 2, 1: 1 6, 2, 2: 4 6, 2, 3: 5 6, 2, 4: 2*q+5 6, 2, 5: 1 6, 2, 6: 2 6, 2, 7: 1 6, 2, 8: 4 6, 3, 1: 2 6, 3, 2: 5 6, 3, 3: 2*q+7 6, 3, 4: 2*q^2+q+6 6, 3, 5: 1 6, 3, 6: 4 6, 3, 7: 2 6, 3, 8: q+5 6, 3, 10: 1 6, 4, 1: 4 6, 4, 2: 2*q+5 6, 4, 3: 2*q^2+q+6 6, 4, 4: 2*q^3+4*q+3 6, 4, 5: 1 6, 4, 6: 3 6, 4, 7: 1 6, 4, 8: 2*q+3 6, 5, 2: 1 6, 5, 3: 1 6, 5, 4: 1 6, 5, 6: 1 6, 5, 8: 1 6, 6, 2: 2 6, 6, 3: 4 6, 6, 4: 3 6, 6, 5: 1 6, 6, 6: 4 6, 6, 7: 2 6, 6, 8: 4 6, 6, 9: 1 6, 6, 10: 1 7, 1, 1: 4 7, 1, 2: 2 7, 1, 3: 1 7, 1, 5: 1 7, 2, 1: 2 7, 2, 2: 3 7, 2, 3: 3 7, 2, 4: 3 7, 2, 5: 1 7, 2, 6: 1 7, 2, 7: 1 7, 2, 8: 1 7, 3, 1: 1 7, 3, 2: 3 7, 3, 3: q+5 7, 3, 4: 2*q+3 7, 3, 5: 1 7, 3, 6: 2 7, 3, 7: 2 7, 3, 8: 2 7, 4, 2: 3 7, 4, 3: 2*q+3 7, 4, 4: 2*q^2+q+5 7, 4, 6: 1 7, 4, 8: q+2 7, 5, 1: 1 7, 5, 2: 1 7, 5, 3: 1 7, 5, 5: 1 7, 5, 7: 1 7, 6, 2: 1 7, 6, 3: 2 7, 6, 4: 1 7, 6, 6: 2 7, 6, 7: 1 7, 6, 8: 2 7, 6, 10: 1 7, 7, 2: 1 7, 7, 3: 2 7, 7, 5: 1 7, 7, 6: 1 7, 7, 7: 2 7, 7, 9: 1 8, 1, 1: -q# NEGATIVE COEFF 8, 1, 3: 4 8, 1, 4: 3*q+3 8, 1, 6: 1 8, 1, 8: 3 8, 2, 2: 5 8, 2, 3: 2*q+7 8, 2, 4: 2*q^2+q+8 8, 2, 6: 4 8, 2, 7: 1 8, 2, 8: q+6 8, 2, 10: 1 8, 3, 1: 4 8, 3, 2: 2*q+7 8, 3, 3: 2*q^2+2*q+8 8, 3, 4: 2*q^3+q^2+4*q+4 8, 3, 5: 1 8, 3, 6: q+5 8, 3, 7: 2 8, 3, 8: q^2+2*q+5 8, 3, 10: 1 8, 4, 1: 3*q+3 8, 4, 2: 2*q^2+q+8 8, 4, 3: 2*q^3+q^2+4*q+4 8, 4, 4: 2*q^4+4*q^2-q+5# NEGATIVE COEFF 8, 4, 5: 3 8, 4, 6: 2*q+3 8, 4, 7: q+2 8, 4, 8: 2*q^2+5 8, 5, 3: 1 8, 5, 4: 3 8, 5, 6: 1 8, 5, 8: 3 8, 5, 10: 1 8, 6, 1: 1 8, 6, 2: 4 8, 6, 3: q+5 8, 6, 4: 2*q+3 8, 6, 5: 1 8, 6, 6: 4 8, 6, 7: 2 8, 6, 8: 2*q+4 8, 6, 10: 1 8, 7, 2: 1 8, 7, 3: 2 8, 7, 4: q+2 8, 7, 6: 2 8, 7, 8: q+3 8, 7, 10: 1 8, 8, 1: 3 8, 8, 2: q+6 8, 8, 3: q^2+2*q+5 8, 8, 4: 2*q^2+5 8, 8, 5: 3 8, 8, 6: 2*q+4 8, 8, 7: q+3 8, 8, 8: 2*q^2+5 8, 8, 9: 1 8, 8, 10: 2 9, 1, 1: 1 9, 2, 2: 1 9, 3, 3: 1 9, 4, 4: 1 9, 5, 5: 1 9, 6, 6: 1 9, 7, 7: 1 9, 8, 8: 1 9, 9, 9: 1 10, 1, 4: 1 10, 2, 3: 1 10, 2, 4: 1 10, 2, 8: 1 10, 3, 2: 1 10, 3, 3: 1 10, 3, 4: 1 10, 3, 6: 1 10, 3, 8: 1 10, 4, 1: 1 10, 4, 2: 1 10, 4, 3: 1 10, 4, 4: 2 10, 5, 8: 1 10, 6, 3: 1 10, 6, 6: 1 10, 6, 7: 1 10, 6, 8: 1 10, 6, 10: 1 10, 7, 6: 1 10, 7, 8: 1 10, 7, 10: 1 10, 8, 2: 1 10, 8, 3: 1 10, 8, 5: 1 10, 8, 6: 1 10, 8, 7: 1 10, 8, 8: 2 10, 9, 10: 1 10, 10, 6: 1 10, 10, 7: 1 10, 10, 9: 1 11, 5, 11: 1 11, 5, 12: 1 11, 7, 12: 1 11, 8, 12: -1# NEGATIVE COEFF 11, 9, 11: 1 11, 11, 5: 1 11, 11, 9: 1 12, 5, 11: 1 12, 5, 12: q+1 12, 6, 12: -1# NEGATIVE COEFF 12, 7, 11: 1 12, 7, 12: 2 12, 8, 11: -1# NEGATIVE COEFF 12, 8, 12: -q+1# NEGATIVE COEFF 12, 9, 12: 1 12, 10, 12: 1 12, 11, 5: 1 12, 11, 7: 1 12, 11, 8: -1# NEGATIVE COEFF 12, 12, 5: q+1 12, 12, 6: -1# NEGATIVE COEFF 12, 12, 7: 2 12, 12, 8: -q+1# NEGATIVE COEFF 12, 12, 9: 1 12, 12, 10: 1
(C) 2005 Frank Lübeck