<font face="Gill Sans,Helvetica,Arial">Unipot</font> is a package for <font face="Gill Sans,Helvetica,Arial">GAP</font>4 <a href="biblio.htm#GAP4"><cite>GAP4</cite></a>. The version 1.0
of this package was the content of my diploma thesis
<a href="biblio.htm#SH2000"><cite>SH2000</cite></a>.
<p>
Let <i>U</i> be a unipotent subgroup of a Chevalley group of Type
<i>L</i>(<i>K</i>). Then it is generated by the elements <i>x</i><sub><i>r</i></sub>(<i>t</i>) for all
<i>r</i> ∈ Φ<sup>+</sup>,<i>t</i> ∈ <i>K</i>. The roots of the underlying root system
Φ are ordered according to the height function. Each
element of <i>U</i> is a product of the root elements <i>x</i><sub><i>r</i></sub>(<i>t</i>). By
Theorem 5.3.3 from <a href="biblio.htm#Car72"><cite>Car72</cite></a> each element of <i>U</i> can be
uniquely written as a product of root elements with roots in
increasing order. This unique form is called the canonical form.
<p>
The main purpose of this package is to compute the canonical form of an element of the group <i>U</i>. For we have implemented the
unipotent subgroups of Chevalley groups and their elements as
<font face="Gill Sans,Helvetica,Arial">GAP</font> objects and installed some operations for them. One
method for the operation <code>Comm</code> uses the Chevalley's commutator
formula, which we have implemented, too.
<p>
<p>
<h2><a name="SECT001">1.1 Root Systems</a></h2>
<p><p>
We are using the root systems and the structure constants
available in <font face="Gill Sans,Helvetica,Arial">GAP</font> from the simple Lie algebras. We also are
using the same ordering of roots available in <font face="Gill Sans,Helvetica,Arial">GAP</font>.
<p>
<p>
<h2><a name="SECT002">1.2 Citing Unipot</a></h2>
<p><p>
If you use <font face="Gill Sans,Helvetica,Arial">Unipot</font> to solve a problem or publish some result
that was partly obtained using <font face="Gill Sans,Helvetica,Arial">Unipot</font>, I would appreciate it
if you would cite <font face="Gill Sans,Helvetica,Arial">Unipot</font>, just as you would citeanother
paper that you used. (Below is a sample citation.) Again I would
appreciate if you could inform me about such a paper.
<p>
Specifically, please refer to:
<p>
<pre>
[Hal02] Sergei Haller. Unipot --- a system for computing with elements
of unipotent subgroups of Chevalley groups, July 2002.
</pre>
<p>
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<P>
<address>unipot manual<br>July 2024
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