mkhom man page

mkhom — calculate homomorphisms between modules

Synopsis

mkhom [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 writes the spinning 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 spinning 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 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 spinning basis.
-s
When M=N, calculate endomorphisms in the spinning basis.
-l
When M=N, find a generating set of End(M), and calculate the left regular representation.
-r
When M=N, find a generating set of End(M), and calculate the right regular representation.
-b
For big endorings, with -r or -l, save memory.
-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 spinning basis for M.
Hom.{1,2,...}
A k-basis of Hom(M,N).
M.std.{1,2,...}
Generators in the spinning basis (with -t).

See Also

chop(1), pwkond(1)

Referenced By

decomp(1).

2.4.24 MeatAxe User Commands