Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



Geometry of weight diagrams for $ {\rm U}(n)$

Author: Eng-Chye Tan
Journal: Trans. Amer. Math. Soc. 336 (1993), 173-192
MSC: Primary 22E46; Secondary 17B10, 20G05
MathSciNet review: 1131077
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [H] James E. Humphreys, Introduction to Lie algebras and representation theory, Springer-Verlag, New York-Berlin, 1972. Graduate Texts in Mathematics, Vol. 9. MR 0323842
  • [M] George W. Mackey, Induced representations of locally compact groups. II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193–221. MR 0056611,
  • [T] E.-C. Tan, On some geometrical properties of $ K$-types of representations, Ph.D. Thesis, Yale Univ., May 1989.
  • [Zh] D. P. Želobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, R.I., 1973. Translated from the Russian by Israel Program for Scientific Translations; Translations of Mathematical Monographs, Vol. 40. MR 0473098

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E46, 17B10, 20G05

Retrieve articles in all journals with MSC: 22E46, 17B10, 20G05

Additional Information

Keywords: Weight diagrams, multiplicity-one weights, $ K$-types, $ K$-type diagrams
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society