#############################################################################
##
#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 CSp_4(q), (2,q) = 1                             #
#                                                                           #
#############################################################################
##
#A {\sc B. Srinivasan},  {\sc K. Shinoda}
#A 
##
lprint(`**************************************************************************`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`*                    Green Functions of CSp_4(q), (2,q) = 1              *`);
lprint(`*                                                                        *`);
lprint(`*                                                                        *`);
lprint(`**************************************************************************`);

# tafel der werte

`C2n2green`:=array(-2..5, -1..5, [

 [`CSp_4(q)`, `C2003green`, q^4*(q-1)^3*(q+1)^2*(q^2+1), 5, 5, 5, 5],
 [`classname`, [``], [`A0`], [`A1`], [`A21`], [`A22`], [`A3`]],

 [`classlength`, 1, 1, (q-1)*(q+1)*(q^2+1), 1/2*q*(q-1)*(q+1)^2*(q^2+1),
  1/2*q*(q-1)^2*(q+1)*(q^2+1), q^2*(q-1)^2*(q+1)^2*(q^2+1)],

 [[[[1,1],[]]], (q+1)^2*(q^2+1), (1+q)^2*(1+q^2), (1+q)^2, 1+3*q, 1+q, 1],

 [[[[1],[1]]], -(q-1)*(q+1)*(q^2+1), -(q-1)*(q+1)*(q^2+1), 1+q^2, 1-q, 1+q, 1],

 [[[[2],[]]], -(q-1)*(q+1)*(q^2+1), -(q-1)*(q+1)*(q^2+1), 1-q^2, 1+q, 1-q, 1],

 [[[[],[1,1]]], (q-1)^2*(q^2+1), (q-1)^2*(q^2+1), (q-1)^2, 1-q, 1-3*q, 1],

 [[[[],[2]]], (q-1)^2*(q+1)^2, (q-1)^2*(q+1)^2, 1-q^2, 1-q, 1+q, 1]       
]):


KlassentypOrdC2003green:=array(1..5,[1,1,1,1,1]):

NurPolynomC2003green:=true:

InformationC2003green:=TEXT(
`- Information about the tables of Green functions for CSp_4(q), q odd.`,
``,
`- CHEVIE-name of the table: C2n2green`,
``,
`- The generic character table of CSp_4(q), q odd, and hence its Green `,
`  functions were computed in:`,
`  {\\sc K.~Shinoda}, The Characters of the Finite Conformal Symplectic`, 
`  Group CSp(4,q), {\\em Comm. Alg.} {\\bf 10(13)} (1982), 1369--1419.`,
``,
`- They can also be read off the table of Sp_4(q), q odd, computed in:`,
`  {\\sc B.~Srinivasan}, The characters of the finite symplectic group`,
`  $Sp(4,q)$, {\\em Trans. Amer. Math. Soc.} {\\bf 131} (1968), 488--525.`,
``,
`- See also:`,
`  {\\sc L.~Lambe and B.~Srinivasan}, A computation of Green functions for`,
`  some classical groups, {\\em Comm. Alg.} {\\bf 18(10)} (1990), 3507--3545.`,
``,
`- The names of the unipotent classes are taken from the article of Shinoda.`,
``):



g:=`C2n2green`:
print(`g := ``C2n2green`` `);
