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On Representations of the Symplectic Group

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Symmetries in Science III
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Abstract

One can consider the compact group Sp(n) as a subgroup of the unitary group U(2n). The imbedding of Sp(n) into U(2n) is given by the isomorphic imbedding of the skew field of quaternions into the linear algebra of 2 × 2 matrices,

\(q = a + bi + cj + dk \to \left( {\frac{z}{{ - w}}\frac{w}{z}} \right),z = a + b;w = c + di\)

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References

  1. W. Rudin, “Function Theory in the Unit Ball of C n ,” Springer, Berlin (1980).

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© 1989 Plenum Press, New York

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Groza, V.A. (1989). On Representations of the Symplectic Group. In: Gruber, B., Iachello, F. (eds) Symmetries in Science III. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0787-7_34

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  • DOI: https://doi.org/10.1007/978-1-4613-0787-7_34

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8082-8

  • Online ISBN: 978-1-4613-0787-7

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