#############################################################################
##
#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 G_2(q),  q = 2^n                                #
#                                                                           #
#############################################################################
##
#A {\sc H. Enomoto, H. Yamada}, The characters of G_2(2^n), Japan J. Math 12
#A   (1986), 325--377
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*                    Green Functions of G_2(q),  q = 2^n                 *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`G2p2green` := array(-2..6, -1..8, [

 [`G_2(q)`, `G2002green`,q^6*(q-1)^2*(q+1)^2*(q^2+q+1)*(q^2-q+1),6,6,8,8],

 [`classname`, [], [`A_{0 }`], [`A_{1 }`], [`A_{2 }`], [`A_{31}`], [`A_{32}`],
  [`A_{4 }`], [`A_{51}`], [`A_{52}`]], 

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

 [[`\\emptyset`], (q+1)^2*(q^2+q+1)*(q^2-q+1), (q+1)^2*(q^2+q+1)*(q^2-q+1),
  (q+1)*(q^2+q+1), (q+1)*(2*q+1), 4*q+1, 2*q+1, q+1, 1, 1], 

 [[`\\tilde A_1`], -(q-1)*(q+1)*(q^2+q+1)*(q^2-q+1), -(q-1)*(q+1)*(q^2+q+1)
  *(q^2-q+1), -(q-1)*(q^2+q+1), q+1, 2*q+1, 1, -q+1, 1, 1], 

 [[`A_1`], -(q-1)*(q+1)*(q^2+q+1)*(q^2-q+1), -(q-1)*(q+1)*(q^2+q+1)*(q^2-q+1),
  (q+1)*(q^2-q+1), -q+1, -2*q+1, 1, q+1, 1, 1], 

 [[`G_2`], (q-1)^2*(q+1)^2*(q^2+q+1), (q-1)^2*(q+1)^2*(q^2+q+1), -(q-1)*(q+1)^2,
  -(q-1)*(q+1), -q+1, q+1, 2*q+1, 1, 1],

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

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


KlassentypOrdG2002green:=array(1..8,[1,1,1,1,1,1,1,1]):

NurPolynomG2002green:=true:

# 5) Informationen:
Information.`G2002green`:=TEXT(
`- Information about the Green functions of $G_2(2^n)$.`,
``,
`- CHEVIE-name of the table: ``G2p2green```,
``,
`- The table was first computed in:`,
`  {\\sc H. Enomoto, H. Yamada}, The characters of $G_2(2^n)$,`,
`    {\\em Japan J. Math \\bf12} (1986), 325--377.`,
``,
`  The notation for the unipotent classes is taken from that paper.`,
``
):

g := `G2p2green`;
print(`g := ``G2p2green`` `);
