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

Referenced By

tuc(1).

2.4.24 MeatAxe User Commands