MeatAxe: tcond - Tensor Product Condensation

MeatAxe 2.4

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tcond - Tensor Product Condensation

## 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 eHaieH on the condensed tensor product (M⊗N)eH.

As input, the program expects the action of ai 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_HaieH on (M⊗N)eH. These matrices are written to Result.1, Result.2 ... If you use the "-t" option, tcond also calculates the action of ai 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".

## Implementation Details

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