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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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Geometry of weight diagrams for $\textrm {U}(n)$
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by Eng-Chye Tan PDF
Trans. Amer. Math. Soc. 336 (1993), 173-192 Request permission

Abstract:

We study the geometry of the weight diagrams for irreducible representations of $U(n)$. Multiplicity-one weights are shown to have nice geometric characterizations. We then apply our results to study multiplicity-one $K$-types of principal representations of $U(n,n)$.
References
  • James E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9, Springer-Verlag, New York-Berlin, 1972. MR 0323842, DOI 10.1007/978-1-4612-6398-2
  • George W. Mackey, Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193–221. MR 56611, DOI 10.2307/1969786
  • E.-C. Tan, On some geometrical properties of $K$-types of representations, Ph.D. Thesis, Yale Univ., May 1989.
  • D. P. Zhelobenko, Kompaktnye gruppy Li i ikh predstavleniya, Izdat. “Nauka”, Moscow, 1970 (Russian). MR 0473097
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 173-192
  • MSC: Primary 22E46; Secondary 17B10, 20G05
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1131077-7
  • MathSciNet review: 1131077