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B.6.0.3 CenCharDec

Procedure from library ncdecomp.lib (see ncdecomp_lib).

Usage:
CenCharDec(I, C); I a module, C a list of generators of the center;

Return:
a list L, where each entry consists of three records:
L[*][1] is the central character in terms of central elements,
L[*][2] is the Groebner basis of the corresponding weight module,
L[*][3] is the K-dimension of the weight module;

Note:
some modules have no finite decomposition (in such case one gets warning message)

Example:
 
LIB "ncdecomp.lib";
option(returnSB);
def a = sl2(); // U(sl_2) in characteristic 0
setring a;
ideal I = e3,f3,h3-4*h;
I = twostd(I);           // two-sided ideal generated by I
vdim(I);                 // it is finite-dimensional
==> 10
list Cn = 4*e*f+h^2-2*h; // the only central element
list T = CenCharDec(I,Cn);
T;
==> [1]:
==>    [1]:
==>       _[1]=4ef+h2-2h-8
==>    [2]:
==>       _[1]=h
==>       _[2]=f
==>       _[3]=e
==>    [3]:
==>       1
==> [2]:
==>    [1]:
==>       _[1]=4ef+h2-2h
==>    [2]:
==>       _[1]=4ef+h2-2h-8
==>       _[2]=h3-4h
==>       _[3]=fh2-2fh
==>       _[4]=eh2+2eh
==>       _[5]=f2h-2f2
==>       _[6]=e2h+2e2
==>       _[7]=f3
==>       _[8]=e3
==>    [3]:
==>       9
CentralQuot, CentralSaturation


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