#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1993,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
# Orthogonalitaet 
#############################################################################
#                                                                           #
#   Die Greenfunktionen der ^3D4(q), (2,q) = 1                              #
#                                                                           #
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##
#A {\sc N. Spaltenstein}, Caract`eres unipotents de $^3D_4(F_q)$, 
#A  Comment. Math. Helvetici 57 (1982), 676--691.
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*             Green Functions of ^3D4(q), (2,q) = 1                      *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`3D4n2green` := array(-2..7,-1..7,[

 [`^3D_4(q)`, `3D4003green`, q^12*(q^8+q^4+1)*(q^6-1)*(q^2-1), 7, 7, 7, 7], 

 [`classname`, [], [`\\emptyset`], [`A1`], [`3A1`], [`A2'`], 
                   [`A2''`],[`D4(a1)`], [`D4`]], 

 [`classlength`, 1, 1, (q^2-1)*(q^8+q^4+1), q^2*(q^6-1)*(q^8+q^4+1),
  q^4*(q^8+q^4+1)*(q^2-1)^2*(q^2-q+1)/2, q^4*(q^8+q^4+1)*(q^2-1)^2*(q^2+q+1)/2,
  q^6*(q^2-1)*(q^6-1)*(q^8+q^4+1), q^8*(q^2-1)*(q^6-1)*(q^8+q^4+1)], 

 [[`~A_2`], (q^2+q+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2,
  (q^2+q+1)*(q^4-q^2+1)*(q+1)^2*(q^2-q+1)^2, (q+1)*(q^2-q+1)*(q^4+q+1),
  (q+1)*(2*q^3+1), 2*q^3+q^2+q+1, (2*q+1)*(q^2-q+1), q+1, 1],

 [[`~A_2+A_1`], -(q^4-q^2+1)*(q^2-q+1)^2*(q+1)*(q^2+q+1)*(q-1),
  -(q^4-q^2+1)*(q^2-q+1)^2*(q+1)*(q^2+q+1)*(q-1), q^7+q^3-q+1, -q+1,
  -q^2-q+1, q^2-q+1, -q+1, 1],

 [[`C_3`], -(q^4-q^2+1)*(q^2+q+1)^2*(q-1)*(q^2-q+1)*(q+1),
  -(q^4-q^2+1)*(q^2+q+1)^2*(q-1)*(q^2-q+1)*(q+1), -q^7-q^3+q+1, q+1,
  q^2+q+1, -q^2+q+1, q+1, 1],

 [[`~A_2+A_2`], (q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2-q+1)^2,
  (q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2-q+1)^2, -(q-1)*(q+1)*(q^2-q+1)*(2*q^3-q^2-q+1),
  -(q+1)*(q-1)^3, 5*q^3-2*q^2-2*q+1, -(q-1)*(q^2-q+1), -2*q+1, 1],

 [[`F_4(a_1)`], (q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2,
  (q^4-q^2+1)*(q-1)^2*(q+1)^2*(q^2+q+1)^2, (q-1)*(q+1)*(q^2+q+1)*(2*q^3+q^2-q-1),
  -(q-1)*(q+1)^3, (q+1)*(q^2+q+1), -5*q^3-2*q^2+2*q+1, 2*q+1, 1],

 [[`F_4`], (q+1)^2*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2,
  (q+1)^2*(q-1)^2*(q^2-q+1)^2*(q^2+q+1)^2, -(q-1)*(q+1)*(q^2+q+1)*(q^2-q+1),
  -(q-1)*(q+1)*(q^2+1), -(q-1)*(q^2+q+1), (q+1)*(q^2-q+1), 1, 1],

 [[`C_3+A_1`], (q^2-q+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2,
  (q^2-q+1)*(q^4-q^2+1)*(q-1)^2*(q^2+q+1)^2, -(q-1)*(q^2+q+1)*(q^4-q+1),
  (q-1)*(2*q^3-1), -(2*q-1)*(q^2+q+1), -2*q^3+q^2-q+1, -q+1, 1]
]):

KlassentypOrd3D4003green:=array(1..7,[1,1,1,1,1,1,1]):

NurPolynom3D4003green:=true:

# 5) Informationen:
Information.`3D4003green`:=TEXT(
`- Information about the Green functions of $^3D_4(q)$, $p>2$.`,
``,
`- CHEVIE-name of the table: ``3D4n2green```,
``,
`- The table was first computed in:`,
`  {\\sc N. Spaltenstein}, Caract``eres unipotents de $^3D_4(F_q)$,`,
`    {\\em Comment. Math. Helvetici \\bf57} (1982), 676--691.`,
``
):

g := `3D4n2green`;
print(`g := ``3D4n2green`` `);



