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
W. Rudin, “Function Theory in the Unit Ball of C n ,” Springer, Berlin (1980).
A. U. Klimyk, A. M. Gavrilik, J. Math. Phys. 20:1624 (1979).
N. Ja. Vilenkin, “Special Functions and the Theory of Group Representations,” Transl. Math. Monogr. 22, Amer. Math. Soc., Providence, R.I. (1968).
M. K. F. Wong, Hsin-Yang Yeh, J. Math. Phys. 21:630 (1980).
A. U. Klimyk, B. Gruber, J. Math. Phys. 25:743 (1984).
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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
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