Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 327-337.

SHARPENING THE DIRAC INEQUALITY

Pavle Pandžić and Ana Prlić

Abstract.   We explain an idea towards a possible proof of a conjecture of Salamanca-Riba and Vogan. This conjecture, also called the Convex hull conjecture, sharpens the well known Dirac inequality of Partahasarathy, which has been useful in several partial classifications of unitary representations of real reductive groups. The idea we present originates from collaboration with David Renard.

2020 Mathematics Subject Classification.   22E47.

Key words and phrases.   Real reductive group, representation, Harish-Chandra module, Dirac operator, Dirac inequality.

DOI: https://doi.org/10.21857/yq32oh8v89

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