MeatAxe: zts - Tensor Split

MeatAxe 2.4

- Main Page
- Related Pages
- Modules
- Data Structures

zts - Tensor Split

## Command Line

    zts Options [-g NumGen] M N Seed [Sub]

Options
  Standard options, see Standard Command Line Options

-g
  Set number of generators (default is 2).

-n --no-action
  Do not calculate the action of the generators on the invariant subspace. Output only the subspace.

M
  First representation (left factor).

N
  Second representation (right factor).

Seed
  Seed vector(s).

Sub
  Invariant subspace. Also used as basename for the action on the invariant subspace.

## Input Files

M.1, M.2, ...
  Generator action on left module. Unless changed with -g, two generators are read.

N.1, N.2, ...
  Generator action on right module

Seed
  Seed vector(s).

## Output Files

Sub
  Basis of the invariant subspace.

Sub.1, Sub.2, ...
  Generator action on the invariant subspace.

See also:
  - tuc - Tensor Uncondense
  - zsp - Spin Up

## Description

This program is similar to zsp, but it works on the tensor product of two modules, M⊗N. zts spins up one or more vectors, and optionally calculates a matrix representation corresponding to the invariant subspace. The program does not use the matrix representation of the generators on M⊗N, which would be too large in many cases. This program is used, for example, to spin up vectors that have been uncondensed with tuc.

The action of the generators on both M and N must be given as square matrices, see "Input Files" above. You can use the -g option to specify the number of generators. The default is two generators.

Seed vectors are read from Seed. They must be given with respect to the lexicographically ordered basis explained below.

If the Sub argument is given, ZTS writes a basis of the invariant subspace to Sub, calculates the action of the generators on the invariant subspace, and writes it to Sub.1, Sub.2,...

## Implementation Details

Let be a basis of M, a basis of N, and denote by the lexicographically ordered basis . For , the coordinate row has entries which can be arranged as a matrix (top to bottom, left to right). Let denote this matrix. Then

Using this relation, we can calculate the image of any vector under an algebra element , and thus spin up a vector without using the matrix representation of on .