#############################################################################
##
#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 GU_4(q)                                         #
#                                                                           #
#############################################################################
##
#A {\sc }, 
#A 
##
lprint(`**********************************************************************\
****`);
lprint(`*                                                                     \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`*                    Green Functions of GU_4(q)                       \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`*                                                                     \
   *`);
lprint(`**********************************************************************\
****`);

GU4green:=array(-2..5, -1..
5   , [
[ `GU_{4}(q)`,   `2A3002green`   ,   (q+1)^4*(q-1)^2*(q^2+1)*q^6*(q^2-q+1)   ,
   5   ,   5   ,   5   ,   5   ],
[``, [
], [   [[1,1,1,1]]
], [   [[2,1,1]]
], [   [[2,2]]
], [   [[3,1]]
], [   [[4]]
] ],
[``, 1
,   1
,   (q+1)*(q-1)*(q^2+1)*(q^2-q+1)
,   (q+1)^2*(q-1)*(q^2+1)*q*(q^2-q+1)
,   (q^2+1)*(q-1)^2*(q+1)^2*q^2*(q^2-q+1)
,   (q^2-q+1)*q^3*(q^2+1)*(q-1)^2*(q+1)^3
]
,[   [[1,1,1,1]]   ,   (q^2+1)*(q^2-q+1)*(q-1)^2
,   (q^2+1)*(q^2-q+1)*(q-1)^2
,   -(q-1)*(3*q^2-2*q+1)
,   (q-1)*(2*q-1)
,   -3*q+1
,   1
]
,[   [[2,1,1]]   ,   -(q+1)*(q-1)*(q^2+1)*(q^2-q+1)
,   -(q+1)*(q-1)*(q^2+1)*(q^2-q+1)
,   q^3+q^2-q+1
,   -q+1
,   -q+1
,   1
]
,[   [[2,2]]   ,   (q^2+1)*(q^2-q+1)*(q+1)^2
,   (q^2+1)*(q^2-q+1)*(q+1)^2
,   (q+1)*(q^2+1)
,   2*q^2+q+1
,   q+1
,   1
]
,[   [[3,1]]   ,   (q^2+1)*(q-1)^2*(q+1)^2
,   (q^2+1)*(q-1)^2*(q+1)^2
,   -(q-1)*(q+1)
,   -(q-1)*(q+1)
,   1
,   1
]
,[   [[4]]   ,   -(q-1)*(q^2-q+1)*(q+1)^3
,   -(q-1)*(q^2-q+1)*(q+1)^3
,   -(q-1)*(q+1)^2
,   q+1
,   q+1
,   1
]
]):

KlassentypOrd2A3002green:=array(1..5,   [1, 1, 1, 1, 1]   ):
NurPolynom2A3002green:=true:
Information2A3002green:=TEXT(
`- Information about the tables of Green functions for GU_4(q^2).`,
``,
`- CHEVIE-name of the table: GU4green`,
``,
`- By a theorem of Hotta, Springer and Kawanaka we can get the Green`,
`  functions of the unitary group GU_4(q^2) from those of GL_4(q) `,
`  by substituting q by -q. This is proved in:`,
`  {\\sc R.~Hotta and T.~A.~Springer}, A specialisation theorem for`,
`  certain Weyl group representations, {\\em Invent. Math.} `,
`  {\\bf 41} (1977), 113--127.`,
`  {\\sc N.~Kawanaka}, Generalized Gelfand--Graev characters and`,
`  Ennola duality, {\\em Adv. Stud. Pure Math.} {\\bf 6} (1985), 175--206.`,
``,
`- See also:`,
`  {\\sc F.~Digne and J.~Michel}, Foncteurs de Lusztig et caract\\``{e}res`,
`  des groupes lin\\'{e}aires et unitaires sur un corps fini, `,
`  {\\em J. of Alg.} {\\bf 107} (1987), 217--255.`,
``,
`- For the computation of the Green functions for GL_n(q) see for example:`,
`  > GreenFunTab(GL2);`,
`  > PrintInfoTab(GL2green);`,
``):
g:=GU4green:
print(`g := ``GU4green`` `);
