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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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