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.

M.rad

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, 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, 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 Szöke [Sz98].