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Low codimensional embeddings of Sp(n) and Su(n)

Published online by Cambridge University Press:  20 January 2009

G. Walker  and
R. M. W. Wood
G. Walker
Affiliation:
University of ManchesterManchester M13 9PL
R. M. W. Wood
Affiliation:
University of ManchesterManchester M13 9PL
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In [4] Elmer Rees proves that the symplectic group Sp(n) can be smoothly embedded in Euclidean space with codimension 3n, and the unitary group U(n) with codimension n. These are special cases of a result he obtains for a compact connected Lie group G. The general technique is first to embed G/T, where T is a maximal torus, as a maximal orbit of the adjoint representation of G, and then to extendto an embedding of G by using a maximal orbit of a faithful representation of G. In thisnote, we observe that in the cases G = Sp(n) or SU(n) an improved result is obtained byusing the “symplectic torus” S3 x … x S3 in place of T = S1 x … x S1. As in Rees's construction, the normal bundle of the embedding of G is trivial.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 27 , Issue 1 , February 1984 , pp. 25 - 29
Copyright
Copyright © Edinburgh Mathematical Society 1984

References

REFERENCES

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