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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Closed product formulas for extensions of generalized Verma modules
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by Riccardo Biagioli PDF
Trans. Amer. Math. Soc. 356 (2004), 159-184 Request permission


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:
  • Received by editor(s): September 24, 2001
  • Received by editor(s) in revised form: February 11, 2002
  • Published electronically: August 26, 2003
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 159-184
  • MSC (2000): Primary 17B10, 05E99; Secondary 22E47, 20F55
  • DOI:
  • MathSciNet review: 2020028