# 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).