Assuming the context node is a service element, you can list the names of the participants like this:
<xsl:for-each select="segments/segment/seats/seat">
<xsl:variable name="p" select="/*/participants/participant[@participantNr = current()/@participantNr]"/>
<xsl:value-of select="$p/name"/>
etc.
If the data file is very large, consider using keys.
Michael Kay
http://www.saxonica.com/
Author, XSLT Programmer's Reference and XPath 2.0 Programmer's Reference