> Now, inside the Slide template, I can access $right, but not $extension.

This would pass parameter with name $extension and value an empty
list 
               <xsl:with-param name="$extension"/>
                                     ^

I would guess that you want to pass a parameter with name extension
and value the value of your extension variable, which is

  <xsl:with-param name="extension" select="$extension"/>
                        ^                  ^


or simpler, not bother with declaring the extension variable at all and
just have the parameter

  <xsl:with-param name="extension" select="'.html'"/>


David


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