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title: "Refining the classification of the irreps of the 1D N-Extended Supersymmetry • CBPF Index"
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**Physics Note****Published**

# **Refining the classification of the irreps of the 1D N-Extended Supersymmetry**

**Zhanna Kuznetsova; F. Toppan**

07/29/2010

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## **Publication details**

<dl>

<dt>Authors</dt>
<dd>Zhanna Kuznetsova; F. Toppan</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>29/07/2010</dd>

<dt>Description</dt>
<dd>In hep-th/0511274 the classification of the fields content of the linear finite irreducible representations of the algebra of the $1D$ $N$-Extended Supersymmetric Quantum Mechanics was given. In hep-th/0611060 it was pointed out that certain irreps with the same fields content can be regarded as inequivalent. This result can be understood in terms of the ``connectivity" properties of the graphs associated to the irreps. We present here a classification of the connectivity of the irreps, refining the hep-th/0511274 classification based on fields content. As a byproduct, we find a counterexample to the hep-th/0611060 claim that the connectivity is uniquely specified by the {\em sources} and {\em targets} of an irrep graph. We produce one pair of $N=5$ irreps and three pairs of $N=6$ irreps with the same number of sources and targets which, nevertheless, differ in connectivity.</dd>

<dt>Year</dt>
<dd>2006</dd>

<dt>Number</dt>
<dd>CBPF-NF-020/06</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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