MeatAxe  2.4 Programs for working with modular representations
mkhom - Homomorphisms

# Command Line

mkhom [Options] [-ts] [-r|-l] [-b Mode] [-H Dim] M N Hom
Options
Standard options, see Standard Command Line Options
-t
Calculate generators for M in spinning basis.
-s
When M equals N, calculate endomorphisms in spinning basis.
-r
When M equals N, find a generating set of End(M), and calculate the right regular representation.
-l
Like -r but calculate the left regular representation.
-b Mode
Save memory. Mode can be 0, 1, or 2 (see description).
-H Dim
If the radical is given, Dim is the dimension of the head.
M
First representation.
N
Second representation.
Hom
Homomorphisms.

# Input Files

M.cfinfo, N.cfinfo
Constituent information.
M.1, M.2,...
Generators in the first representation.
N.1, N.2,...
Generators in the second representation.
Generators for the head of M (with -H).
MCf.k
Uncondense matrix produced by pwkond.

# Output Files

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

# Description

This program calculates a basis for the vector space of homomorphisms between two kG-modules, HomkG(M,N). In the case M=N the program optionally finds a generating set for the algebra of endomoprhisms, EndkG(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, 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 and pwkond must have been run on the first module.

# Implementation Details

The algorithm used by this program was developed by Magdolna SzĂ¶ke [Sz98].

MeatAxe 2.4 documentation, generated on Wed Jan 7 2015 08:38:36