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