I am looking for a reference that gives the definition and has summarized the dual Coxeter number for superalgebras, especially for $\mathfrak{u}(m|n)$ (the Lie algebra of unitary supergroup $U(m|n)$).
$\begingroup$
$\endgroup$
$\begingroup$
$\endgroup$
The dual Coxeter number for basic Lie superalgebras is given in the table on page 16 of Kostant’s cubic Dirac operator of Lie superalgebras. Also, the generalization of the Freudenthal-de Vries strange formula holds for Lie superalgebras as well (equation (38) of the above reference).
-
$\begingroup$ What is the definition of "dual Coxeter element" here? Meanwhile, here is a more detailed description of Kostant's own article: mathscinet.ams.org/mathscinet-getitem?mr=1719734 $\endgroup$ – Jim Humphreys Jan 16 '18 at 16:50
