#############################################################################
##
#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_4(q)                  \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`**********************************************************************\
****`);
`uniGL4`   :=array(-2..5,-1..23,[
[`GL_4(q)`,`uniA3002`
,   q^6*(q^2+1)*(q^2+q+1)*(q+1)^2*(q-1)^4
,   5
,   5
,   23
,   23
]
,[
``,``,
[`A_3(q)`,   q-1   ,   [[1, 1, 1, 1]]   ]
,
[`A_3(q)`,   q-1   ,   [[2, 1, 1]]   ]
,
[`A_3(q)`,   q-1   ,   [[2, 2]]   ]
,
[`A_3(q)`,   q-1   ,   [[3, 1]]   ]
,
[`A_3(q)`,   q-1   ,   [[4]]   ]
,
[`A_2(q)`,   (q-1)^2   ,   [[1, 1, 1]]   ]
,
[`A_2(q)`,   (q-1)^2   ,   [[2, 1]]   ]
,
[`A_2(q)`,   (q-1)^2   ,   [[3]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^2   ,   [[1, 1], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^2   ,   [[1, 1], [2]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^2   ,   [[2], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^2   ,   [[2], [2]]   ]
,
[`A_1(q^2)`,   (q-1)*(q+1)   ,   [[1, 1]]   ]
,
[`A_1(q^2)`,   (q-1)*(q+1)   ,   [[2]]   ]
,
[`A_1(q)`,   (q-1)^3   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q-1)^3   ,   [[2]]   ]
,
[`A_1(q)`,   (q+1)*(q-1)^2   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q+1)*(q-1)^2   ,   [[2]]   ]
,
[`\\emptyset`,   (q-1)^4   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)*(q-1)^3   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)^2*(q+1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q^2+q+1)*(q-1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)*(q+1)*(q^2+1)   ,   [[[1]], 1]   ]
]
,[
erg[0,-1]   ,
erg[0,0]   ,
1   ,
q^6+q^5+q^4-q^2-q-1   ,
q^8-q^5-q^4+q   ,
q^10+q^9-q^7-2*q^6-q^5+q^3+q^2   ,
q^12-q^10-q^9-q^8+q^7+q^6+q^5-q^3   ,
(q+1)*(q^2+1)*q^3   ,
(q^4+q^3-q-1)*(q+1)*(q^2+1)*q^3   ,
(q^6-q^4-q^3+q)*(q+1)*(q^2+1)*q^3   ,
(q^2+1)*(q^2+q+1)*q^4   ,
(q^2-1)*(q^2+1)*(q^2+q+1)*q^4   ,
(q^2-1)*(q^2+1)*(q^2+q+1)*q^4   ,
(q^4-2*q^2+1)*(q^2+1)*(q^2+q+1)*q^4   ,
(q^2+q+1)*(q-1)^2*q^4   ,
(q^4-1)*(q^2+q+1)*(q-1)^2*q^4   ,
(q+1)*(q^2+q+1)*(q^2+1)*q^5   ,
(q^2-1)*(q+1)*(q^2+q+1)*(q^2+1)*q^5   ,
(q-1)*(q^2+q+1)*(q^2+1)*q^5   ,
(q^2-1)*(q-1)*(q^2+q+1)*(q^2+1)*q^5   ,
(q^2+q+1)*(q^2+1)*(q+1)^2*q^6   ,
(q-1)*(q+1)*(q^2+q+1)*(q^2+1)*q^6   ,
(q^2+q+1)*(q^2+1)*(q-1)^2*q^6   ,
(q^2+1)*(q-1)^2*(q+1)^2*q^6   ,
(q+1)*(q^2+q+1)*(q-1)^3*q^6   ]
,[
[[1, 1, 1, 1]]   ,
q^6   ,
q^6   ,
0   ,
0   ,
0   ,
0   ,
q^3   ,
0   ,
0   ,
q^2   ,
0   ,
0   ,
0   ,
q^2   ,
0   ,
q   ,
0   ,
-q   ,
0   ,
1   ,
-1   ,
1   ,
1   ,
-1   ]
,[
[[2, 1, 1]]   ,
q^3*(q^2+q+1)   ,
q^3*(q^2+q+1)   ,
q^3   ,
0   ,
0   ,
0   ,
q*(q^2+q+1)   ,
q   ,
0   ,
q*(q+2)   ,
q   ,
q   ,
0   ,
-q^2   ,
0   ,
2*q+1   ,
1   ,
-1   ,
-1   ,
3   ,
-1   ,
-1   ,
0   ,
1   ]
,[
[[2, 2]]   ,
q^2*(q^2+1)   ,
q^2*(q^2+1)   ,
q^2   ,
q^2   ,
0   ,
0   ,
(q+1)*q   ,
q   ,
0   ,
q^2+1   ,
1   ,
1   ,
1   ,
q^2+1   ,
1   ,
q+1   ,
1   ,
-q+1   ,
1   ,
2   ,
0   ,
2   ,
-1   ,
0   ]
,[
[[3, 1]]   ,
q*(q^2+q+1)   ,
q*(q^2+q+1)   ,
(q+1)*q   ,
q   ,
q   ,
0   ,
q^2+q+1   ,
q+1   ,
1   ,
2*q+1   ,
q+1   ,
q+1   ,
1   ,
-1   ,
-1   ,
q+2   ,
2   ,
q   ,
0   ,
3   ,
1   ,
-1   ,
0   ,
-1   ]
,[
[[4]]   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ]
]):
KlassentypOrduniA3002:=   [q-1, q-1, q-1, q-1, q-1, q^2-3*q+2, q^2-3*q+2, q^2-3
*q+2, 1/2*q^2-3/2*q+1, 1/2*q^2-3/2*q+1, 1/2*q^2-3/2*q+1, 1/2*q^2-3/2*q+1, 1/2*q
^2-1/2*q, 1/2*q^2-1/2*q, 1/2*q^3-3*q^2+11/2*q-3, 1/2*q^3-3*q^2+11/2*q-3, 1/2*q^
3-q^2+1/2*q, 1/2*q^3-q^2+1/2*q, 1/24*q^4-5/12*q^3+35/24*q^2-25/12*q+1, 1/4*q^4-
q^3+5/4*q^2-1/2*q, 1/8*q^4-1/4*q^3-1/8*q^2+1/4*q, 1/3*q^4-1/3*q^3-1/3*q^2+1/3*q
, 1/4*q^4-1/4*q^2]   :
NurPolynomuniA3002:=true:
InformationuniA3002:=TEXT(
`- Information about the tables of unipotent characters for GL_4(q).`,
``,
`- CHEVIE-name of the table: uniGL4`,
``,
`- 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:=`uniGL4`:
print(` g := ``uniGL4`` `);
