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 $U(m|n)$).
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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).
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1$\begingroup$ 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 $\endgroup$ Commented Jan 16, 2018 at 16:50