Geometry of weight diagrams for $\textrm {U}(n)$
HTML articles powered by AMS MathViewer
- by Eng-Chye Tan
- Trans. Amer. Math. Soc. 336 (1993), 173-192
- DOI: https://doi.org/10.1090/S0002-9947-1993-1131077-7
- PDF | 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
Bibliographic 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