Command Line

tcond [Options] [-nt] [-T MaxTime] [-g NGen] Info M N Result

Options: Standard options, see Standard Command Line Options

-g NGen: Set the number of generators. Default is 2.

-n: No basis change. Assume that the generators on M and N are already given with respect to the semisimplicity basis.

-t: Write out transformed generators for M and N.

Info: Information produced by precond.

M: Name of the first representation (left factor).

N: Name of the second representation (right factor).

Result: Condensed representation.

Input Files

Info.tki: Tensor condensation info, made by precond.

M.1, M.2, ...: Generators of left factor.

N.1, N.2, ...: Generators of right factor.

M.ssb: Semisimplicity basis for M, made by pwkond.

N.ssb: Semisimplicity basis for N, made by pwkond.

Info.q.1, Info.q.2, ...: Basis matrices for constituents.

Info.p.1, Info.p.2,: Projection matrices for constituents.

Output Files

Result.1, Result.2, ...: Condensed matrices.

M.ss.1, M.ss.2, ...: Transformed generators (with -t)

N.ss.1, N.ss.2, ...: Transformed generators (with -t)

Description

This program performs the final steps of the tensor condensation procedure. It calculates, for one or more elements a₁,a₂,…∊A, the action of e_Ha_ie_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 output are NGen matrices describing the action of e__Ha_ie_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 more simple, 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".

Implementatin Details

The algorithm used by this program is described in [Wie94].