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Abstract
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The Schur orthogonality relations for finite-dimensional representations are
generalized to weight modules of complex reductive Lie algebras by establishing the
equality of the Euler–Poincaré pairing and the spinor pairing. We also show how to
calculate these pairings by using Dirac cohomology.
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Keywords
Dirac cohomology, weight module, Euler–Poincaré pairing,
spinor pairing
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Mathematical Subject Classification
Primary: 17B10
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Milestones
Received: 16 March 2022
Revised: 27 May 2022
Accepted: 4 June 2022
Published: 28 August 2022
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