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