mkhom_old man page

mkhom_old — calculate homomorphisms between modules


mkhom_old [Options] <M> <N> <Hom>


This program calculates a basis for the vector space of homomorphisms between two kG-modules, Hom_kG(M,N).  In the case M=N the program optionally finds a generating set for the algebra of endomoprhisms, End_kG(M), and calculates the corresponding left or right regular representation.

If used without any options, mkhom_old writes the standard basis of M to M.std, and a k-basis of the homomorphism space to Hom.1, Hom.2, ....  The latter are given with respect to the standard basis of M and the original basis of N.  To get the homomorphisms with respect to the original bases of M and N]fP, multiply the matrices from the left with the inverse of Hom.

Mkhom_old uses peak words of the first module.  Thus, before using the program, chop(1) and pwkond(1) must have been run on the first module.



Quiet, no messages.


Verbose, more messages.

-T <MaxTime>

Set CPU time limit


Calculate generators for <M> in the standard basis.


When M=N, calculate endomorphisms in the standard basis.

-r <Side>

When M=N, find a generating set of End(M), and calculate the left (Side=1) or right (Side=2) regular representation.

-b <Mode>

Save memory, Mode=0..2.

-H <Dim>

If the radical is given, Dim is the dimension of the head.

Implementation Details

The algorithm used by this program was developed by Magdolna Szöke; see "Examining Green Correspondents of Weight Modules", Aachener Beiträge zur Mathematik, Band 24, Wissenschaftsverlag Mainz, Aachen, 1998.

Input Files


Generators in representation M.


Generators in representation N.


Constituent info file for M.


Constituent info file for N.


Generators for the head of M (with -H).


Uncondense matrix, produced by pwkond(1).

Output Files


The standard basis for M.


A k-basis of Hom(M,N).


Generators in the standard basis (with -t).

See Also

chop(1), pwkond(1)


2.4.24 MeatAxe User Commands