#############################################################################
##
#F                             CHEVIE library
##
#Y  Copyright 1992--1993,  Lehrstuhl D f"ur Mathematik,    RWTH Aachen,   and
#Y                         IWR   der   Universit"at    Heidelberg,   Germany.
##
#############################################################################
#                                                                           #
#   Die Greenfunktionen der GL_5(q)                                         #
#                                                                           #
#############################################################################
##
#A {\sc }, 
#A 
##
lprint(`**********************************************************************\
****`);
lprint(`*                                                                     \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`*                    Green Functions of GL_5(q)                       \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`**********************************************************************\
****`);

GL5green:=array(-2..7, -1..
7   , [
[ `GL_{5}(q)`,   A4002green   ,   (q-1)^5*(q^4+q^3+q^2+q+1)*q^10*(q+1)^2*(q^2+1
)*(q^2+q+1)   ,   7   ,   7   ,   7   ,   7   ],
[``, [
], [   [[1,1,1,1,1]]
], [   [[2,1,1,1]]
], [   [[2,2,1]]
], [   [[3,1,1]]
], [   [[3,2]]
], [   [[4,1]]
], [   [[5]]
] ],
[``, 1
,   1
,   (q-1)*(q^4+q^3+q^2+q+1)*(q+1)*(q^2+1)
,   (q-1)^2*(q^4+q^3+q^2+q+1)*q*(q+1)*(q^2+1)*(q^2+q+1)
,   (q-1)^2*(q^4+q^3+q^2+q+1)*q^3*(q+1)*(q^2+1)*(q^2+q+1)
,   (q-1)^3*(q^4+q^3+q^2+q+1)*q^3*(q+1)^2*(q^2+1)*(q^2+q+1)
,   (q-1)^3*(q^4+q^3+q^2+q+1)*q^5*(q+1)^2*(q^2+1)*(q^2+q+1)
,   (q-1)^4*(q^4+q^3+q^2+q+1)*q^6*(q+1)^2*(q^2+1)*(q^2+q+1)
]
,[   [[1,1,1,1,1]]   ,   (q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q+1)^2
,   (q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q+1)^2
,   (q+1)*(q^2+q+1)*(4*q^3+3*q^2+2*q+1)
,   (q+1)*(5*q^3+6*q^2+3*q+1)
,   (q+1)*(6*q^2+3*q+1)
,   5*q^2+4*q+1
,   4*q+1
,   1
]
,[   [[2,1,1,1]]   ,   -(q-1)*(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)
,   -(q-1)*(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)
,   -(q^2+q+1)*(2*q^4-q^3-q^2-q-1)
,   -(q+1)*(q^3-2*q^2-q-1)
,   3*q^2+2*q+1
,   (q+1)^2
,   2*q+1
,   1
]
,[   [[2,2,1]]   ,   (q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q-1)^2
,   (q^2+q+1)*(q^4+q^3+q^2+q+1)*(q^2+1)*(q-1)^2
,   -(q-1)*(q^2+1)*(q^2+q+1)
,   q^4-q^3+q^2+1
,   -(q-1)*(2*q^2+q+1)
,   q^2+1
,   1
,   1
]
,[   [[3,1,1]]   ,   (q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*(q+1)^2
,   (q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^2*(q+1)^2
,   (q-1)*(q+1)*(q^4-q^3-q^2-q-1)
,   -(q-1)*(q+1)*(q^2+q+1)
,   q+1
,   -q^2+q+1
,   q+1
,   1
]
,[   [[3,2]]   ,   -(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^3
,   -(q+1)*(q^2+1)*(q^4+q^3+q^2+q+1)*(q-1)^3
,   (q^4+q^3+q^2+q+1)*(q-1)^2
,   -(q-1)*(q+1)*(q^2-q+1)
,   -q+1
,   q^2-q+1
,   -q+1
,   1
]
,[   [[4,1]]   ,   -(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q-1)^3
,   -(q+1)*(q^2+q+1)*(q^4+q^3+q^2+q+1)*(q-1)^3
,   (q+1)*(q^2+q+1)*(q-1)^2
,   (q-1)*(q^3-q-1)
,   -(q-1)*(q+1)
,   -(q-1)*(q+1)
,   1
,   1
]
,[   [[5]]   ,   (q^2+q+1)*(q^2+1)*(q+1)^2*(q-1)^4
,   (q^2+q+1)*(q^2+1)*(q+1)^2*(q-1)^4
,   -(q+1)*(q^2+q+1)*(q-1)^3
,   (q+1)*(q-1)^2
,   (q+1)*(q-1)^2
,   -q+1
,   -q+1
,   1
]
]):

KlassentypOrdA4002green:=array(1..7,   [1, 1, 1, 1, 1, 1, 1]   ):
NurPolynomA4002green:=true:
InformationA4002green:=TEXT(
`- Information about the tables of Green functions for GL_5(q).`,
``,
`- CHEVIE-name of the table: GL5green`,
``,
`- These Green functions were introduced in:`,
`  {\\sc J.~A.~Green}, The characters of the finite general linear`,
`  groups, {\\em Trans. Amer. Math. Soc.} {\\bf 80} (1955), 402--447.`,
``,
`- See also:`,
`  {\\sc R.~Steinberg}, The representations of $GL(3,q)$,  $GL(4,q)$, $PGL(3,q\
)$ `,
`  and $PGL(4,q)$, {\\em Can. J. of Math.} {\\bf 3} (1951), 225--235.`,
``,
`- This CHEVIE-table is computed by an algorithm from `,
`  the following article:`,
`  {\\sc A.~Lascoux and M.~P.~Sch{\\"u}tzenberger}, Sur une conjecture de `,
`  H.~O.~Foulkes, {\\em C. R. Acad. Sci. Paris} {\\bf 286A}  (1978), 323--324.\
`,
``,
`- The program which generates the files with the Green functions `,
`  of GL_n(q) and GU_n(q) is part of the CHEVIE-system. You `,
`  can reproduce them with the CHEVIE commands: `,
`  > GreenFunctionsA(n,filename);`,
`  > GreenFunctions2A(n,filename);`,
`  (see the corresponding help)`,
`  These programs are written by U. Porsch and F. Luebeck.`,
``):
g:=GL5green:
print(`g := ``GL5green`` `);
