# tcond man page

tcond — tensor product condensation

## Synopsis

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

## Description

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".

## Options

**-Q**- Quiet, no messages.
**-V**- Verbose, more messages.
**-T***<MaxTime>*- Set CPU time limit
**-g***<NGen>*- Set the number of generators. Default: 2.
**-t**- Write transformed generators of
*<A>*and*<B>*. **-n**- 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

*Info*.tki- Tensor condensation information, made by precond(1).
*A*.{1,2,...}- Generators of the left factor.
*B*.{1,2,...}- Generators of the right factor.
*A*.ssb- Semisimplicity basis for
*A*, made by pwkond(1). *B*.ssb- Semisimplicity basis for
*B*, made by pwkond(1). *Info*.q.{1,2,...}- Basis matrices for constituents.
*Info*.p.{1,2,...}- Projection matrices for constituents.

## Output Files

*Result*.{1,2,...}- Condensed matrices.
*A*.ss.{1,2,...}- Transformed generators (with -t).
*B*.ss.{1,2,...}- Transformed generators (with -t).

## See Also

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