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 Free Access

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. Zhelobenko, \cyr Kompaktnye gruppy Li i ikh predstavleniya., Izdat. “Nauka”, Moscow, 1970 (Russian). MR 0473097
    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