#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1994,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
#############################################################################

olprint(`**********************************************************************\
****`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                    Unipotent characters of GL_3(q)                  \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`**********************************************************************\
****`);
`uniGL3`   :=array(-2..3,-1..8,[
[`GL_3(q)`,`uniA2002`
,   q^3*(q+1)*(q^2+q+1)*(q-1)^3
,   3
,   3
,   8
,   8
]
,[
``,``,
[`A_2(q)`,   q-1   ,   [[1, 1, 1]]   ]
,
[`A_2(q)`,   q-1   ,   [[2, 1]]   ]
,
[`A_2(q)`,   q-1   ,   [[3]]   ]
,
[`A_1(q)`,   (q-1)^2   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q-1)^2   ,   [[2]]   ]
,
[`\\emptyset`,   (q-1)^3   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)*(q-1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)*(q^2+q+1)   ,   [[[1]], 1]   ]
]
,[
erg[0,-1]   ,
erg[0,0]   ,
1   ,
q^4+q^3-q-1   ,
q^6-q^4-q^3+q   ,
(q^2+q+1)*q^2   ,
(q^2-1)*(q^2+q+1)*q^2   ,
(q+1)*(q^2+q+1)*q^3   ,
(q-1)*(q^2+q+1)*q^3   ,
(q+1)*(q-1)^2*q^3   ]
,[
[[1, 1, 1]]   ,
q^3   ,
q^3   ,
0   ,
0   ,
q   ,
0   ,
1   ,
-1   ,
1   ]
,[
[[2, 1]]   ,
(q+1)*q   ,
(q+1)*q   ,
q   ,
0   ,
q+1   ,
1   ,
2   ,
0   ,
-1   ]
,[
[[3]]   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ]
]):
KlassentypOrduniA2002:=   [q-1, q-1, q-1, q^2-3*q+2, q^2-3*q+2, 1/6*q^3-q^2+11/
6*q-1, 1/2*q^3-q^2+1/2*q, 1/3*q^3-1/3*q]   :
NurPolynomuniA2002:=true:
InformationuniA2002:=TEXT(
`- Information about the tables of unipotent characters for GL_3(q).`,
``,
`- CHEVIE-name of the table: uniGL3`,
``,
`- This table is computed with general programs written by F.Luebeck.`,
`  They compute the Deligne-Lusztig characters R_T^G(1) and find the`,
`  unipotent characters as linear combinations of them.`,
``):

g:=`uniGL3`:
print(` g := ``uniGL3`` `);
