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##
#F                             CHEVIE library
##
#Y  Copyright 1992--1993,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
# orthogonalitaet o.k. uep 10.2.92
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#                                                                           #
#   Die Greenfunktionen der Sp_6(q),  q = 2^n                               #
#                                                                           #
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##
#A {\sc }, 
#A 
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*                    Green Functions of Sp_6(q), q = 2^n                 *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`C3p2green`  := array(-2..10, -1..12, [

 [`Sp_6(q)`, `C3002green` , q^9*(q-1)^3*(q+1)^3*(q^2+q+1)*(q^2+1)*(q^2-q+1),
   10, 10, 12, 12],

 [`classes`, ` `, `u_0`, `u_1`, `u_2`, `u_3`, `u_4`, `u_5`, `u_6`, `u_7`,
  `u_8`, `u_9`, `u_{10}`, `u_{11}` ],

 [`classlenghts`, 1, 1, (q-1)*(q+1)*(q^2-q+1)*(q^2+q+1),
  (q+1)*(q^2-q+1)*(q^2+q+1)*(q-1)*(q^2+1),
  (q+1)^2*(q^2-q+1)*(q^2+q+1)*(q-1)^2*(q^2+1),
  q^2*(q+1)^2*(q^2-q+1)*(q^2+q+1)*(q-1)^2*(q^2+1),
  1/2*(q-1)^2*(q+1)^3*(q^2+1)*(q^2-q+1)*(q^2+q+1)*q^3,
  1/2*(q-1)^3*(q+1)^2*(q^2+1)*(q^2-q+1)*(q^2+q+1)*q^3,
  1/2*q^4*(q+1)^2*(q^2-q+1)*(q^2+q+1)*(q-1)^2*(q^2+1),
  1/2*q^4*(q+1)^2*(q^2-q+1)*(q^2+q+1)*(q-1)^2*(q^2+1),
  q^4*(q-1)^3*(q+1)^3*(q^2-q+1)*(q^2+q+1)*(q^2+1),
  1/2*q^6*(q-1)^3*(q+1)^3*(q^2-q+1)*(q^2+q+1)*(q^2+1),
  1/2*q^6*(q-1)^3*(q+1)^3*(q^2-q+1)*(q^2+q+1)*(q^2+1)],

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

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

 [[[[2,1],[]]],-(q-1)*(q+1)^2*(q^2+q+1)*(q^2+1)*(q^2-q+1),
  -(q-1)*(q+1)^2*(q^2+q+1)*(q^2+1)*(q^2-q+1), -(q-1)*(q+1)*(q^2+q+1)*(q^2+1),
  (q+1)*(q^2+1), -(q+1)*(q^3-q^2-1), -q^3+q^2+q+1, 2*q^2+q+1, q+1, q+1, q+1, q+1,
  1, 1],

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

 [[[[2],[1]]],(q-1)^2*(q+1)*(q^2+q+1)*(q^2+1)*(q^2-q+1),
  (q-1)^2*(q+1)*(q^2+q+1)*(q^2+1)*(q^2-q+1), -(q-1)*(q+1)*(q^2+1)*(q^2-q+1),
  -(q-1)*(q^2+1), -(q-1)*(q^3+q^2+1), q^3+q^2-q+1, -q+1, 2*q^2-q+1, -q+1,
  -q+1, -q+1, 1, 1],

 [[[[1],[2]]],(q-1)^2*(q+1)^3*(q^2+q+1)*(q^2-q+1),
  (q-1)^2*(q+1)^3*(q^2+q+1)*(q^2-q+1), -(q-1)*(q+1)^3*(q^2-q+1),
  -(q-1)*(q+1)^2, (q+1)*(q^3-q^2+1), -(q-1)*(q+1)^2, -(q-1)*(2*q+1),
  q+1, q+1, q+1, q+1, 1, 1],

 [[[[3],[]]],(q-1)^2*(q+1)^3*(q^2+1)*(q^2-q+1),
  (q-1)^2*(q+1)^3*(q^2+1)*(q^2-q+1), (q-1)^2*(q+1)^2*(q^2+1),
  -(q-1)*(q+1)^2*(q^2-q+1), -(q-1)*(q+1), -(q-1)*(q+1), q^2+1, -(q-1)*(q+1),
  -(q-1)*(q+1), -(q-1)*(q+1), 1, 1, 1],

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

 [[[[],[2,1]]],-(q-1)^3*(q+1)^2*(q^2+q+1)*(q^2-q+1),
  -(q-1)^3*(q+1)^2*(q^2+q+1)*(q^2-q+1), -(q-1)^3*(q+1)*(q^2+q+1),
  (q+1)*(q-1)^2, (q-1)*(q^3+q^2-1), (q+1)*(q-1)^2, -q+1, -(q+1)*(2*q-1),
  -q+1, -q+1, -q+1, 1, 1],

 [[[[],[3]]],-(q-1)^3*(q+1)^2*(q^2+q+1)*(q^2+1),
  -(q-1)^3*(q+1)^2*(q^2+q+1)*(q^2+1), (q-1)^2*(q+1)^2*(q^2+1),
  (q-1)^2*(q+1)*(q^2+q+1), -(q-1)*(q+1), -(q-1)*(q+1), -(q-1)*(q+1),
  q^2+1, -(q-1)*(q+1), -(q-1)*(q+1), 1, 1, 1]]
):

KlassentypOrdC3002green:=array(1..12,[1,1,1,1,1,1,1,1,1,1,1,1]):

NurPolynomC3002green:=true:

# 5) Informationen:
Information.`C3002green`:=TEXT(
`- Information about the Green functions of $Sp_6(2^n)$.`,
``,
`- CHEVIE-name of the table: ``C3p2green```,
``,
`- The table was published in:`,
`  {\\sc G. Malle}, Green functions for groups of types E_6 and F_4 in`,
`  characteristic 2, {\\em Comm. Algebra} {\\bf21} (1993), 747--798.`,
``,
`- The unipotent classes were determined in:`,
`  {\\sc K. Shinoda}, The conjugacy classes of Chevalley groups of type,`,
`  $(F_4)$ over finite fields of characteristic 2, {\\em J. Fac Sci`,
`  Univ. Tokyo} {\\bf21} (1974), 133--159.`,
``,
`- The notation for the unipotent classes is taken from that paper.`,
``
):

g := `C3p2green`;
print(`g := ``C3p2green`` `);


