#############################################################################
##
#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 = 3^n                                #
#                                                                           #
#############################################################################
##
#A {\sc H. Enomoto}, The characters of the finite Chevalley groups G_2(q), 
#A   q=3^f, Japann J. Math. 2 (1976), 191--248
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*                    Green Functions of G_2(q),  q = 3^n                 *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`G2p3green` := array(-2..6, -1..9, [

 [`G_2(q)`, `G2003green`, q^6*(q-1)^2*(q+1)^2*(q^2+q+1)*(q^2-q+1), 6, 6, 9, 9],

 [`classname`, [], [`A_{1 }`], [`A_{2 }`], [`A_{31}`], [`A_{32}`], [`A_{41}`],
  [`A_{42}`], [`A_{51}`], [`A_{52}`], [`A_{53}`]], 

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


KlassentypOrdG2003green:=array(1..9,[1,1,1,1,1,1,1,1,1]):

NurPolynomG2003green:=true:

# 5) Informationen:
Information.`G2003green`:=TEXT(
`- Information about the Green functions of $G_2(3^n)$.`,
``,
`- CHEVIE-name of the table: ``G2p3green```,
``,
`- The table was first computed in:`,
`  {\\sc H. Enomoto}, The characters of the finite Chevalley groups $G_2(q)$,`,
`    $q=3^f$, {\\em Japann J. Math. \\bf2} (1976), 191--248.`,
``,
`  The notation for the unipotent classes is taken from that paper.`,
``
):

g := `G2p3green`;
print(`g := ``G2p3green`` `);
