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Let Hg and Dg be the Siegel upper half plane and the generalized
unit disk of degree g respectively. Let C(h,g) be the Euclidean
space of all h × g complex matrices. We present a partial Cayley transform
of the Siegel–Jacobi disk Dg × C(h,g) onto the Siegel–Jacobi space
Hg × C(h,g) which gives a partial bounded realization of Hg × C(h,g) by
Dg × C(h,g). We prove that the natural actions of the Jacobi group on
Dg×C(h,g) and Hg×C(h,g) are compatible via a partial Cayley transform.
A partial Cayley transform plays an important role in computing differential
operators on the Siegel–Jacobi disk Dg ×C(h,g) invariant under the
natural action of the Jacobi group on Dg × C(h,g) explicitly.
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참고문헌 (17)
참고문헌 신청
A. Koranyi / 1965 / Generalized Cayley transformations of bounded symmetric domains / American Journal of Mathematics 87 : 899 ~ 939
A. W. Knapp / 1986 / Representation Theory of Semisimple Groups / Princeton University Press
C. L. Siegel / 1943 / Symplectic geometry / American Journal of Mathematics 65 : 1 ~ 86
C. Ziegler / 1989 / Jacobi forms of higher degree / Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 59 : 191 ~ 224
H. Maass / 1953 / Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen / Mathematische Annalen 126 : 44 ~ 68
A. W. Knapp / 1986 / Representation Theory of Semisimple Groups / Princeton University Press
C. L. Siegel / 1943 / Symplectic geometry / American Journal of Mathematics 65 : 1 ~ 86
C. Ziegler / 1989 / Jacobi forms of higher degree / Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg 59 : 191 ~ 224
H. Maass / 1953 / Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen / Mathematische Annalen 126 : 44 ~ 68
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