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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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First layer formulas for characters of $\textrm {SL}(n,\textbf {C})$
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by John R. Stembridge PDF
Trans. Amer. Math. Soc. 299 (1987), 319-350 Request permission


Some problems concerning the decomposition of certain characters of $SL(n, {\mathbf {C}})$ are studied from a combinatorial point of view. The specific characters considered include those of the exterior and symmetric algebras of the adjoint representation and the Euler characteristic of Hanlon’s so-called “Macdonald complex.” A general recursion is given for computing the irreducible decomposition of these characters. The recursion is explicitly solved for the first layer representations, which are the irreducible representations corresponding to partitions of $n$. In the case of the exterior algebra, this settles a conjecture of Gupta and Hanlon. A further application of the recursion is used to give a family of formal Laurent series identities that generalize the (equal parameter) $q$-Dyson Theorem.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 299 (1987), 319-350
  • MSC: Primary 20G05; Secondary 05A15, 17B10, 22E46
  • DOI:
  • MathSciNet review: 869415