tcond man page

tcond — tensor product condensation


tcond [Options] <Info> <A> <B> <Result>


This program performs the final steps of the tensor condensation procedure. It calculates, for one or more elements a_1, a_2, ... , the action of e_H·a_i·e_H on the condensed tensor product (M⊗N)e_H.

As input, the program expects the action of a_i on M and N with respect to the same basis as the generators of the condensation subgroup H that were fed into precond before.  The program also needs the semisimplicity basis calculated by pwkond, and the P and Q matrices calculated by precond.

If the generators are already given with repect to the semisimplicity basis, you can use the -n option to tell tcond to skip the basis change.

The outputs are NGen matrices describing the action of e_H·a_i·e_H on (M⊗N)e_H.  These matrices are written to Result.1, Result.2, ....  If you use the -t option, tcond also calculates the action of a_i on M and N with respect to the semisimplicity basis.  This option cannot be used together with -n.

The following sequence of commands shows the complete procedure for condensing a tensor product.  To make things simpler, we assume that M=N.  The condensation subgroup shall be given by three generators in the files "sub.1", "sub.2", and "sub.3".  The generators of the group shall be "g.1" and "g.2".

chop -g 3 sub
pwkond -tb sub
precond tp sub sub
tcond -g 2 tp g g result

After these commands are completed, the action of the condensed generators is in "result.1", "result.2", and "result.3".



Quiet, no messages.


Verbose, more messages.

-T <MaxTime>

Set CPU time limit

-g <NGen>

Set the number of generators.  Default: 2.


Write transformed generators of <A> and <B>.


No basis change.  Assume that generators on <A> and <B> are already in semisimplicity basis.

Implementation Details

The algorithm used by this program is described in Markus Wiegelmann, "Fixpunktkondensation von Tensorproduktmoduln", Diplomarbeit, Lehrstuhl D für Mathematik der RWTH Aachen, 1994.

Input Files


Tensor condensation information, made by precond(1).


Generators of the left factor.


Generators of the right factor.


Semisimplicity basis for A, made by pwkond(1).


Semisimplicity basis for B, made by pwkond(1).


Basis matrices for constituents.


Projection matrices for constituents.

Output Files


Condensed matrices.{1,2,...}

Transformed generators (with -t).{1,2,...}

Transformed generators (with -t).

See Also

chop(1), precond(1), pwkond, tuc

Referenced By


2.4.24 MeatAxe User Commands