The names Leipoxais, Arpoxais and Kolaxais
are analysable as (and usually taken to be) compounds with the second element a
derivative of *xs^ayati 'rule'. The connection of Kolaxais, the youngest of the
three, with the Paralatai suggests that the <-l-> in his name
reflects lambdacised *-ry-. One possible etymology is *xWa:rya-xs^aya-, where
*xWa:rya- is a vrddhied adjective based on *xWar- 'sun, glow', with the
hypothetical meaning 'solar, radiant'. A related alternative is substantivised
*xWa:rya:- 'radiance, glory' > *xWala- (perhaps the source of Slavic *xvala,
according to Gol/a,b 1973). The Greek refashioning of *xWala-xs^aya- as
<kolaksai-> (with Iranian labialisation responsible for the Greek rounded
vowel) is quite plausible. The names of the elder brothers are more enigmatic.
Perhaps (forgive sheer speculation) <arpo-> reflects *arba- < I-Ir.
*arbHa- < *orbHo- 'orphan; slave, labourer'; <leipo-> beats me entirely
at present.
Piotr