mkhom_old man page

mkhom_old — calculate homomorphisms between modules

Synopsis

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

Description

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.

Options

-Q
Quiet, no messages.
-V
Verbose, more messages.
-T <MaxTime>
Set CPU time limit
-t
Calculate generators for <M> in the standard basis.
-s
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

M.{1,2,...}
Generators in representation M.
N.{1,2,...}
Generators in representation N.
M.cfinfo
Constituent info file for M.
N.cfinfo
Constituent info file for N.
M.rad
Generators for the head of M (with -H).
M<Cf>.k
Uncondense matrix, produced by pwkond(1).

Output Files

M.std
The standard basis for M.
Hom.{1,2,...}
A k-basis of Hom(M,N).
M.std.{1,2,...}
Generators in the standard basis (with -t).

See Also

chop(1), pwkond(1)

Info

2.4.24 MeatAxe User Commands