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- W2891546058 abstract "We present a closed formula, analogous to the Weyl dimension formula, for the signature of an invariant Hermitian form on any finite-dimensional irreducible representation of a real reductive Lie group, assuming that such a form exists. The formula shows in a precise sense that the form must be very indefinite. For example, if an irreducible representation of $GL(n,R)$ admits an invariant form of signature $(p,q)$, then we show that $(p-q)^2 le p+q$. The proof is an application of Kostant's computation of the kernel of the Dirac operator." @default.
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- W2891546058 date "2018-09-10" @default.
- W2891546058 modified "2023-09-27" @default.
- W2891546058 title "Signatures for finite-dimensional representations of real reductive Lie groups" @default.
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