Closed product formulas for extensions of generalized Verma modules

Biagioli, Riccardo

doi:10.1090/S0002-9947-03-03037-X

Closed product formulas for extensions of generalized Verma modules
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by Riccardo Biagioli

Trans. Amer. Math. Soc. 356 (2004), 159-184

DOI: https://doi.org/10.1090/S0002-9947-03-03037-X

Published electronically: August 26, 2003

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Abstract:

We give explicit combinatorial product formulas for the polynomials encoding the dimensions of the spaces of extensions of $(g,p)$-generalized Verma modules, in the cases when $(g,p)$ corresponds to an indecomposable classic Hermitian symmetric pair. The formulas imply that these dimensions are combinatorial invariants. We also discuss how these polynomials, defined by Shelton, are related to the parabolic $R$-polynomials introduced by Deodhar.

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