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Closed product formulas for extensions of generalized Verma modules


Author: Riccardo Biagioli
Journal: Trans. Amer. Math. Soc. 356 (2004), 159-184
MSC (2000): Primary 17B10, 05E99; Secondary 22E47, 20F55
DOI: https://doi.org/10.1090/S0002-9947-03-03037-X
Published electronically: August 26, 2003
MathSciNet review: 2020028
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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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Additional Information

Riccardo Biagioli
Affiliation: Dipartimento di Matematica, Università di Roma “La Sapienza”, 00185 Roma, Italy
Address at time of publication: LACIM, Université du Quebéc à Montréal, case postale 8888, succursale Centre-Ville, Montréal, Quebéc, Canada H3C 3P8
Email: biagioli@math.uqam.ca

DOI: https://doi.org/10.1090/S0002-9947-03-03037-X
Received by editor(s): September 24, 2001
Received by editor(s) in revised form: February 11, 2002
Published electronically: August 26, 2003
Article copyright: © Copyright 2003 American Mathematical Society

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