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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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Extensions of Verma modules
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by Kevin J. Carlin PDF
Trans. Amer. Math. Soc. 294 (1986), 29-43 Request permission

Abstract:

A spectral sequence is introduced which computes extensions in category $\mathcal {O}$ in terms of derived functors associated to coherent translation functors. This is applied to the problem of computing extensions of one Verma module by another when the highest weights are integral and regular. Some results are obtained which are consistent with the Gabber-Joseph conjecture. The main result is that the highest-degree nonzero extension is one-dimensional. The spectral sequence is also applied to the Kazhdan-Lusztig conjecture and related to the work of Vogan in this area.
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 294 (1986), 29-43
  • MSC: Primary 17B10; Secondary 17B20, 22E47
  • DOI: https://doi.org/10.1090/S0002-9947-1986-0819933-4
  • MathSciNet review: 819933