#############################################################################
##
#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_5(q)                  \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`*                                                                     \
   *`);
olprint(`**********************************************************************\
****`);
`uniGL5`   :=array(-2..7,-1..43,[
[`GL_5(q)`,`uniA4002`
,   q^10*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q+1)^2*(q-1)^5
,   7
,   7
,   43
,   43
]
,[
``,``,
[`A_4(q)`,   q-1   ,   [[1, 1, 1, 1, 1]]   ]
,
[`A_4(q)`,   q-1   ,   [[2, 1, 1, 1]]   ]
,
[`A_4(q)`,   q-1   ,   [[2, 2, 1]]   ]
,
[`A_4(q)`,   q-1   ,   [[3, 1, 1]]   ]
,
[`A_4(q)`,   q-1   ,   [[3, 2]]   ]
,
[`A_4(q)`,   q-1   ,   [[4, 1]]   ]
,
[`A_4(q)`,   q-1   ,   [[5]]   ]
,
[`A_3(q)`,   (q-1)^2   ,   [[1, 1, 1, 1]]   ]
,
[`A_3(q)`,   (q-1)^2   ,   [[2, 1, 1]]   ]
,
[`A_3(q)`,   (q-1)^2   ,   [[2, 2]]   ]
,
[`A_3(q)`,   (q-1)^2   ,   [[3, 1]]   ]
,
[`A_3(q)`,   (q-1)^2   ,   [[4]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[1, 1, 1], [1, 1]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[1, 1, 1], [2]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[2, 1], [1, 1]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[2, 1], [2]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[3], [1, 1]]   ]
,
[`A_2(q)+A_1(q)`,   (q-1)^2   ,   [[3], [2]]   ]
,
[`A_2(q)`,   (q-1)^3   ,   [[1, 1, 1]]   ]
,
[`A_2(q)`,   (q-1)^3   ,   [[2, 1]]   ]
,
[`A_2(q)`,   (q-1)^3   ,   [[3]]   ]
,
[`A_2(q)`,   (q+1)*(q-1)^2   ,   [[1, 1, 1]]   ]
,
[`A_2(q)`,   (q+1)*(q-1)^2   ,   [[2, 1]]   ]
,
[`A_2(q)`,   (q+1)*(q-1)^2   ,   [[3]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^3   ,   [[1, 1], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^3   ,   [[1, 1], [2]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^3   ,   [[2], [1, 1]]   ]
,
[`A_1(q)+A_1(q)`,   (q-1)^3   ,   [[2], [2]]   ]
,
[`A_1(q^2)`,   (q+1)*(q-1)^2   ,   [[1, 1]]   ]
,
[`A_1(q^2)`,   (q+1)*(q-1)^2   ,   [[2]]   ]
,
[`A_1(q)`,   (q-1)^4   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q-1)^4   ,   [[2]]   ]
,
[`A_1(q)`,   (q+1)*(q-1)^3   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q+1)*(q-1)^3   ,   [[2]]   ]
,
[`A_1(q)`,   (q^2+q+1)*(q-1)^2   ,   [[1, 1]]   ]
,
[`A_1(q)`,   (q^2+q+1)*(q-1)^2   ,   [[2]]   ]
,
[`\\emptyset`,   (q-1)^5   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)*(q-1)^4   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)^2*(q-1)^3   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q^2+q+1)*(q-1)^3   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)*(q^2+q+1)*(q-1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q+1)*(q^2+1)*(q-1)^2   ,   [[[1]], 1]   ]
,
[`\\emptyset`,   (q-1)*(q^4+q^3+q^2+q+1)   ,   [[[1]], 1]   ]
]
,[
erg[0,-1]   ,
erg[0,0]   ,
1   ,
q^8+q^7+q^6+q^5-q^3-q^2-q-1   ,
q^12+q^11+q^10-q^8-2*q^7-2*q^6-q^5+q^3+q^2+q   ,
q^14+q^13+q^12-q^10-2*q^9-2*q^8-q^7+q^5+q^4+q^3   ,
q^16+q^15-q^13-2*q^12-2*q^11-q^10+q^9+2*q^8+2*q^7+q^6-q^4-q^3   ,
q^18+q^17-q^15-2*q^14-2*q^13-q^12+q^11+2*q^10+2*q^9+q^8-q^6-q^5   ,
q^20-q^18-q^17-q^16+q^14+2*q^13+q^12-q^10-q^9-q^8+q^6   ,
(q^4+q^3+q^2+q+1)*q^4   ,
(q^6+q^5+q^4-q^2-q-1)*(q^4+q^3+q^2+q+1)*q^4   ,
(q^8-q^5-q^4+q)*(q^4+q^3+q^2+q+1)*q^4   ,
(q^10+q^9-q^7-2*q^6-q^5+q^3+q^2)*(q^4+q^3+q^2+q+1)*q^4   ,
(q^12-q^10-q^9-q^8+q^7+q^6+q^5-q^3)*(q^4+q^3+q^2+q+1)*q^4   ,
(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q^2-1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q^4+q^3-q-1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q^6+q^5-q^4-2*q^3-q^2+q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q^6-q^4-q^3+q)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q^8-2*q^6-q^5+q^4+2*q^3-q)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^6   ,
(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q^4+q^3-q-1)*(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q^6-q^4-q^3+q)*(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q-1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q^4+q^3-q-1)*(q-1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q^6-q^4-q^3+q)*(q-1)*(q^2+1)*(q^4+q^3+q^2+q+1)*q^7   ,
(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^8   ,
(q^2-1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^8   ,
(q^2-1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^8   ,
(q^4-2*q^2+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^8   ,
(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*q^8   ,
(q^4-1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*q^8   ,
(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^9   ,
(q^2-1)*(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^9   ,
(q-1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^9   ,
(q^2-1)*(q-1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^9   ,
(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*q^9   ,
(q^2-1)*(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*q^9   ,
(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q+1)^2*q^10   ,
(q-1)*(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*q^10   ,
(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q-1)^2*q^10   ,
(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*(q+1)^2*q^10   ,
(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^3*q^10   ,
(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q-1)^3*q^10   ,
(q^2+1)*(q^2+q+1)*(q+1)^2*(q-1)^4*q^10   ]
,[
[[1, 1, 1, 1, 1]]   ,
q^10   ,
q^10   ,
0   ,
0   ,
0   ,
0   ,
0   ,
0   ,
q^6   ,
0   ,
0   ,
0   ,
0   ,
q^4   ,
0   ,
0   ,
0   ,
0   ,
0   ,
q^3   ,
0   ,
0   ,
-q^3   ,
0   ,
0   ,
q^2   ,
0   ,
0   ,
0   ,
q^2   ,
0   ,
q   ,
0   ,
-q   ,
0   ,
q   ,
0   ,
1   ,
-1   ,
1   ,
1   ,
-1   ,
-1   ,
1   ]
,[
[[2, 1, 1, 1]]   ,
q^6*(q+1)*(q^2+1)   ,
q^6*(q+1)*(q^2+1)   ,
q^6   ,
0   ,
0   ,
0   ,
0   ,
0   ,
(q+1)*(q^2+1)*q^3   ,
q^3   ,
0   ,
0   ,
0   ,
q^2*(q+1)^2   ,
q^3   ,
q^2   ,
0   ,
0   ,
0   ,
q*(2*q^2+q+1)   ,
q   ,
0   ,
-(q+1)*q   ,
-q   ,
0   ,
2*(q+1)*q   ,
q   ,
q   ,
0   ,
0   ,
0   ,
3*q+1   ,
1   ,
-q-1   ,
-1   ,
1   ,
1   ,
4   ,
-2   ,
0   ,
1   ,
1   ,
0   ,
-1   ]
,[
[[2, 2, 1]]   ,
(q^4+q^3+q^2+q+1)*q^4   ,
(q^4+q^3+q^2+q+1)*q^4   ,
q^4*(q+1)   ,
q^4   ,
0   ,
0   ,
0   ,
0   ,
q^2*(q^3+2*q^2+q+1)   ,
q^2*(q+1)   ,
q^2   ,
0   ,
0   ,
q*(q^3+q^2+2*q+1)   ,
(q+1)*q   ,
(q+1)*q   ,
q   ,
0   ,
0   ,
q*(q^2+2*q+2)   ,
2*q   ,
0   ,
-q^3   ,
0   ,
0   ,
2*q^2+2*q+1   ,
q+1   ,
q+1   ,
1   ,
1   ,
1   ,
3*q+2   ,
2   ,
-q   ,
0   ,
-1   ,
-1   ,
5   ,
-1   ,
1   ,
-1   ,
-1   ,
1   ,
0   ]
,[
[[3, 1, 1]]   ,
q^3*(q^2+1)*(q^2+q+1)   ,
q^3*(q^2+1)*(q^2+q+1)   ,
q^3*(q^2+q+1)   ,
q^3   ,
q^3   ,
0   ,
0   ,
0   ,
q*(q^2+1)*(q^2+q+1)   ,
q*(q^2+q+1)   ,
q   ,
q   ,
0   ,
2*q*(q^2+q+1)   ,
q*(q^2+q+1)   ,
q*(q+2)   ,
q   ,
q   ,
0   ,
(q+1)*(q^2+q+1)   ,
2*q+1   ,
1   ,
(q-1)*(q^2+q+1)   ,
-1   ,
-1   ,
q^2+4*q+1   ,
2*q+1   ,
2*q+1   ,
1   ,
-q^2-1   ,
-1   ,
3*q+3   ,
3   ,
q-1   ,
-1   ,
0   ,
0   ,
6   ,
0   ,
-2   ,
0   ,
0   ,
0   ,
1   ]
,[
[[3, 2]]   ,
q^2*(q^4+q^3+q^2+q+1)   ,
q^2*(q^4+q^3+q^2+q+1)   ,
(q^2+q+1)*q^2   ,
q^2*(q+1)   ,
q^2   ,
q^2   ,
0   ,
0   ,
q*(q^3+q^2+2*q+1)   ,
q*(2*q+1)   ,
(q+1)*q   ,
q   ,
0   ,
q^3+2*q^2+q+1   ,
q^2+q+1   ,
q^2+q+1   ,
q+1   ,
1   ,
1   ,
2*q^2+2*q+1   ,
2*q+1   ,
1   ,
1   ,
1   ,
1   ,
q^2+2*q+2   ,
q+2   ,
q+2   ,
2   ,
q^2   ,
0   ,
2*q+3   ,
3   ,
1   ,
1   ,
-q   ,
0   ,
5   ,
1   ,
1   ,
-1   ,
1   ,
-1   ,
0   ]
,[
[[4, 1]]   ,
q*(q+1)*(q^2+1)   ,
q*(q+1)*(q^2+1)   ,
q*(q^2+q+1)   ,
(q+1)*q   ,
(q+1)*q   ,
q   ,
q   ,
0   ,
(q+1)*(q^2+1)   ,
q^2+q+1   ,
q+1   ,
q+1   ,
1   ,
(q+1)^2   ,
q^2+q+1   ,
2*q+1   ,
q+1   ,
q+1   ,
1   ,
q^2+q+2   ,
q+2   ,
2   ,
(q+1)*q   ,
q   ,
0   ,
2*q+2   ,
q+2   ,
q+2   ,
2   ,
0   ,
0   ,
q+3   ,
3   ,
q+1   ,
1   ,
q   ,
0   ,
4   ,
2   ,
0   ,
1   ,
-1   ,
0   ,
-1   ]
,[
[[5]]   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ,
1   ]
]):
KlassentypOrduniA4002:=   [q-1, q-1, 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, q^2-3*q+2, q^2-3*q+2, q^2-3*q+2, q^2-3*q+2, q^2-3*q+2, q^2-3*q+
2, q^2-3*q+2, q^2-3*q+2, 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^
3-3*q^2+11/2*q-3, 1/2*q^3-q^2+1/2*q, 1/2*q^3-q^2+1/2*q, 1/2*q^3-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^3-3*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, 1/6*q^4-5/3*q^3+35/6*q^2-25/
3*q+4, 1/6*q^4-5/3*q^3+35/6*q^2-25/3*q+4, 1/2*q^4-2*q^3+5/2*q^2-q, 1/2*q^4-2*q^
3+5/2*q^2-q, 1/3*q^4-1/3*q^3-1/3*q^2+1/3*q, 1/3*q^4-1/3*q^3-1/3*q^2+1/3*q, 1/
120*q^5-1/8*q^4+17/24*q^3-15/8*q^2+137/60*q-1, 1/12*q^5-7/12*q^4+17/12*q^3-17/
12*q^2+1/2*q, 1/8*q^5-3/8*q^4+1/8*q^3+3/8*q^2-1/4*q, 1/6*q^5-1/2*q^4+1/6*q^3+1/
2*q^2-1/3*q, 1/6*q^5-1/6*q^4-1/6*q^3+1/6*q^2, 1/4*q^5-1/4*q^4-1/4*q^3+1/4*q^2, 
1/5*q^5-1/5*q]   :
NurPolynomuniA4002:=true:
InformationuniA4002:=TEXT(
`- Information about the tables of unipotent characters for GL_5(q).`,
``,
`- CHEVIE-name of the table: uniGL5`,
``,
`- 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:=`uniGL5`:
print(` g := ``uniGL5`` `);
