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Orbits and characters associated to highest weight representations

Author: David H. Collingwood
Journal: Proc. Amer. Math. Soc. 114 (1992), 1157-1165
MSC: Primary 22E47; Secondary 17B10, 20G05, 22E46
MathSciNet review: 1074750
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Abstract: We relate two different orbit decompositions of the flag variety. This allows us to pass from the closed formulas of Boe, Enright, and Shelton for the formal character of an irreducible highest weight representation to closed formulas for the distributional character written as a sum of characters of generalized principal series representations. Otherwise put, we give a dictionary between certain Lusztig-Vogan polynomials arising in Harish-Chandra module theory and the Kazhdan-Lusztig polynomials associated to a relative category $ \mathcal{O}$ of Hermitian symmetric type.

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