#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1994,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
#############################################################################
#                                                                           #
#   Die Greenfunktionen der O_8^-(q) in guter Charakteristik                #
#                                                                           #
#############################################################################
##
printf("**************************************************************************\n");
printf("*                                                                        *\n");
printf("*                                                                        *\n");
printf("*                    Green Functions of O_8^-(q), q odd                  *\n");
printf("*                                                                        *\n");
printf("*                                                                        *\n");
printf("**************************************************************************\n");


`2D4n2green`:=array(-2..9,-1..9,[
[`^2D_4(q)`, `2D4003green`, q^28 - q^26 - q^22 + q^18 + q^14 - q^12,9,9,9,9],
[ ``, ``, [ [ 1, 1, 1, 1, 1, 1, 1, 1 ] ], [ [ 2, 2, 1, 1, 1, 1 ] ], [ [ 3, 1, \
1, 1, 1, 1 ] ], [ [ 3, 2, 2, 1 ] ], [ [ [ 3, 3, 1, 1 ] ], 1 ], [ [ [ 3, 3, 1, \
1 ] ], 2 ], [ [ 5, 1, 1, 1 ] ], [ [ 5, 3 ] ], [ [ 7, 1 ] ] ],
[ 0, 0, q^0, q^10 + q^6 - q^4 - 1, q^12 + q^8 - q^6 - q^2, 
  q^16 - q^10 - q^8 + q^2, (1/2)*q^18 + (-1/2)*q^12 + (-1/2)*q^10 + (1/2)*q^4,
  (1/2)*q^18 + (-1/2)*q^12 + (-1/2)*q^10 + (1/2)*q^4, 
  q^20 - q^14 - q^12 + q^6, q^22 - q^20 - q^16 + q^12 + q^8 - q^6, 
  q^24 - q^22 - q^18 + q^14 + q^10 - q^8 ],
[ 0, 0, q^12 + 2*q^11 + 3*q^10 + 4*q^9 + 5*q^8 + 6*q^7 + 6*q^6 + 6*q^5 + 5*q^
    4 + 4*q^3 + 3*q^2 + 2*q + 1, 2*q^7 + 3*q^6 + 4*q^5 + 5*q^4 + 4*q^3 + 3*q^
    2 + 2*q + 1, 3*q^6 + 4*q^5 + 5*q^4 + 6*q^3 + 3*q^2 + 2*q + 1, 
  2*q^4 + 4*q^3 + 3*q^2 + 2*q + 1, 4*q^3 + 5*q^2 + 2*q + 1, 
  4*q^3 + q^2 + 2*q + 1, 3*q^2 + 2*q + 1, 2*q + 1, q^0 ],
[ 0, 0, q^12 - 2*q^11 + 3*q^10 - 4*q^9 + 5*q^8 - 6*q^7 + 6*q^6 - 6*q^5 + 5*q^
    4 - 4*q^3 + 3*q^2 - 2*q + 1, -2*q^7 + 3*q^6 - 4*q^5 + 5*q^4 - 4*q^3 + 3*q^
    2 - 2*q + 1, 3*q^6 - 4*q^5 + 5*q^4 - 6*q^3 + 3*q^2 - 2*q + 1, 
  2*q^4 - 4*q^3 + 3*q^2 - 2*q + 1, -4*q^3 + q^2 - 2*q + 1, 
  -4*q^3 + 5*q^2 - 2*q + 1, 3*q^2 - 2*q + 1, -2*q + 1, q^0 ],
[ 0, 0, -q^12 - 2*q^11 - q^10 - q^8 - 2*q^7 + 2*q^5 + q^4 + q^2 + 2*q + 1, 
  -2*q^7 - 3*q^6 + q^4 + q^2 + 2*q + 1, -q^6 + 3*q^4 + 2*q^3 + q^2 + 2*q + 1, 
  q^2 + 2*q + 1, 2*q^3 + 3*q^2 + 2*q + 1, -2*q^3 - q^2 + 2*q + 1, 
  q^2 + 2*q + 1, 2*q + 1, q^0 ],
[ 0, 0, -q^12 - q^10 - q^8 + q^4 + q^2 + 1, q^6 + q^4 + q^2 + 1, 
  -q^6 - q^4 + q^2 + 1, q^2 + 1, -2*q^3 + q^2 + 1, 2*q^3 + q^2 + 1, q^2 + 1, 
  q^0, q^0 ],
[ 0, 0, -q^12 + 2*q^11 - q^10 - q^8 + 2*q^7 - 2*q^5 + q^4 + q^2 - 2*q + 1, 
  2*q^7 - 3*q^6 + q^4 + q^2 - 2*q + 1, -q^6 + 3*q^4 - 2*q^3 + q^2 - 2*q + 1, 
  q^2 - 2*q + 1, 2*q^3 - q^2 - 2*q + 1, -2*q^3 + 3*q^2 - 2*q + 1, 
  q^2 - 2*q + 1, -2*q + 1, q^0 ],
[ 0, 0, q^12 - q^10 + q^8 - 2*q^6 + q^4 - q^2 + 1, -q^6 + q^4 - q^2 + 1, 
  -q^6 + q^4 - q^2 + 1, 2*q^4 - q^2 + 1, -q^2 + 1, -q^2 + 1, -q^2 + 1, q^0, 
  q^0 ],
[ 0, 0, q^12 + q^11 - q^9 - q^8 - q^4 - q^3 + q + 1, 
  q^7 - q^5 - q^4 - q^3 + q + 1, -q^5 - q^4 + q + 1, -q^4 - q^3 + q + 1, 
  -q^3 + q^2 + q + 1, -q^3 - q^2 + q + 1, q + 1, q + 1, q^0 ],
[ 0, 0, q^12 - q^11 + q^9 - q^8 - q^4 + q^3 - q + 1, 
  -q^7 + q^5 - q^4 + q^3 - q + 1, q^5 - q^4 - q + 1, -q^4 + q^3 - q + 1, 
  q^3 - q^2 - q + 1, q^3 + q^2 - q + 1, -q + 1, -q + 1, q^0 ],
[ 0, 0, -q^12 + q^10 + q^8 - q^4 - q^2 + 1, q^6 - q^4 - q^2 + 1, 
  q^6 - q^4 - q^2 + 1, -q^2 + 1, -q^2 + 1, -q^2 + 1, -q^2 + 1, q^0, q^0 ]
]):
`2D4n2green`[1,-1]:=[[ [ D, 0 ] ],[ [[ 1, 1, 1 ],[ 1 ]] ]]:
`2D4n2green`[2,-1]:=[[ [ D, 0 ] ],[ [[ 1 ],[ 1, 1, 1 ]] ]]:
`2D4n2green`[3,-1]:=[[ [ D, 0 ] ],[ [[ 1, 1 ],[ 2 ]] ]]:
`2D4n2green`[4,-1]:=[[ [ D, 0 ] ],[ [[ 2, 1 ],[ 1 ]] ]]:
`2D4n2green`[5,-1]:=[[ [ D, 0 ] ],[ [[],[ 2, 1, 1 ]] ]]:
`2D4n2green`[6,-1]:=[[ [ D, 0 ] ],[ [[ 2 ],[ 2 ]] ]]:
`2D4n2green`[7,-1]:=[[ [ D, 0 ] ],[ [[ 1 ],[ 3 ]] ]]:
`2D4n2green`[8,-1]:=[[ [ D, 0 ] ],[ [[ 3 ],[ 1 ]] ]]:
`2D4n2green`[9,-1]:=[[ [ D, 0 ] ],[ [[],[ 4 ]] ]]:

KlassentypOrd2D4003green:=array(1..9,[ 1, 1, 1, 1, 1, 1, 1, 1, 1 ]):

NurPolynom2D4003green:=true:

Information2D4003green:=TEXT(
`- Information about the Green functions of $O_8^-(q)$ with odd $q$.`,
``,
`- CHEVIE-name of the table: ``2D4n2green```,
``,
`- This table of generalized Green functions is computed by F.Luebeck `,
`  using Lusztig's algorithm.`,``,
`- The occuring Levi subgroups have the following relative (twisted)`,
`  Weyl groups:`,
`      Levi L                           type of N(L)/L`,
`[ [ D, 0 ] ]           [ [ D, 4, 2 ] ]`,
``,
`- Position [-1,-1] contains the transformation matrix to the`,
`  Foulkes functions and [0,-1] the corresponding labels.`,
``):
`2D4n2green`[-1,-1]:=array(
[ [ 1/48, 1/48, -1/16, -1/8, -1/16, 1/8, 1/6, 1/6, -1/4 ], 
  [ 1/24, -1/24, -1/8, 0, 1/8, 0, 1/6, -1/6, 0 ], 
  [ 1/16, 1/16, -1/16, -1/8, -1/16, -1/8, 0, 0, 1/4 ], 
  [ 1/24, 1/24, 0, 0, 0, 1/4, -1/6, -1/6, 0 ], 
  [ 1/12, -1/12, 0, 0, 0, 0, -1/6, 1/6, 0 ], 
  [ 0, 0, -1/8, 1/4, -1/8, 0, 0, 0, 0 ], 
  [ 1/16, 1/16, 1/16, 1/8, 1/16, -1/8, 0, 0, -1/4 ], 
  [ 1/24, -1/24, 1/8, 0, -1/8, 0, 1/6, -1/6, 0 ], 
  [ 1/48, 1/48, 1/16, 1/8, 1/16, 1/8, 1/6, 1/6, 1/4 ] ]):
`2D4n2green`[0,-1]:=[ [ [ [ D, 0 ] ], [ [[ 1, 1, 1, 1 ],[]] ] ], [ [ [ D, 0 ] \
], [ [[ 1, 1, 1 ],[ 1 ]] ] ], [ [ [ D, 0 ] ], [ [[ 2, 1, 1 ],[]] ] ], [ [ [ D,\
 0 ] ], [ [[ 2, 2 ],[]] ] ], [ [ [ D, 0 ] ], [ [[ 2, 1 ],[ 1 ]] ] ], [ [ [ D, \
0 ] ], [ [[ 1, 1 ],[ 2 ]] ] ], [ [ [ D, 0 ] ], [ [[ 3, 1 ],[]] ] ], [ [ [ D, 0\
 ] ], [ [[ 3 ],[ 1 ]] ] ], [ [ [ D, 0 ] ], [ [[ 4 ],[]] ] ] ]:

g := `2D4n2green`;
print(`g := ``2D4n2green`` `);
