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Let $n \geq 3$ be fixed. We associate to every subset $S \subseteq \{1,...,n-1 \}$ a number, which we call Cartan determinant of $S$ (see the end of this post for a representation theoretic background)...

In a computation of characters of certain representations of finite cyclic groups which appear as equivariant indices of Dirac operators (using the Atiyah-Bott fixed point formula, cf. [1, Theorem 8....