Acknowledgement
Supported by : National Research Foundation of Korea (NRF)
References
- R. Berndt and R. Schmidt, Elements of the Representation Theory of the Jacobi Group, Birkhauser, 1998.
- M. Eichler and D. Zagier, The Theory of Jacobi Forms, Progress in Math., 55, Birkhauser, Boston, Basel and Stuttgart, 1985.
- E. Freitag, Siegelsche Modulfunktionen, Grundlehren de mathematischen Wissenschaften 55, Springer-Verlag, Berlin-Heidelberg-New York, 1983.
- S. Gelbart, Weil's Representation and the Spectrum of the Metaplectic Group, Lecture Notes in Math. 530, Springer-Verlag, Berlin and New York, 1976.
- T. Ibukiyama, On Jacobi forms and Siegel modular forms of half integral weights, Comment. Math. Univ. St. Paul. 41 (1992), no. 2, 109-124.
- T. Ikeda, On the lifting of elliptic cusp forms to Siegel cusp forms of degree 2n, Ann. of Math. 154 (2001), no. 3, 641-681. https://doi.org/10.2307/3062143
- M. Itoh, H. Ochiai, and J.-H. Yang, Invariant differential operators on Siegel-Jacobi space, preprint, 2013.
- M. Kashiwara and M. Vergne, On the Segal-Shale-Weil representations and harmonic polynomials, Invent. Math. 44 (1978), no. 1, 1-47. https://doi.org/10.1007/BF01389900
- G. Lion and M. Vergne, The Weil representation, Maslov index and Theta series, Progress in Math., 6, Birkhauser, Boston, Basel and Stuttgart, 1980.
- G. W. Mackey, Induced representations of locally compact groups. I, Ann. of Math. 55 (1952), 101-139. https://doi.org/10.2307/1969423
- J. Marklof, Pair correlation densities of inhomogeneous quadratic forms, Ann. of Math. 158 (2003), no. 2, 419-471. https://doi.org/10.4007/annals.2003.158.419
- D. Mumford, Tata Lectures on Theta. I, Progress in Math. 28, Boston-Basel-Stuttgart, 1983.
- A. Pitale, Jacobi Maass forms, Abh. Math. Sem. Univ. Hamburg 79 (2009), no. 1, 87-111. https://doi.org/10.1007/s12188-008-0013-9
- C. L. Siegel, Indefinite quadratische Formen und Funnktionentheorie I and II, Math. Ann. 124 (1951), 17-54 and Math. Ann. 124 (1952), 364-387 https://doi.org/10.1007/BF01343549
- C. L. Siegel, Gesammelte Abhandlungen, Band III, Springer-Verlag (1966), 105-142 and 154-177
- K. Takase, A note on automorphic forms, J. Reine Angew. Math. 409 (1990), 138-171.
- K. Takase, On two-fold covering group of Sp(n,R) and automorphic factor of weight 1/2, Comment. Math. Univ. St. Paul. 45 (1996), no. 2, 117-145.
- K. Takase, On Siegel modular forms of half-integral weights and Jacobi forms, Trans. Amer. Math. Soc. 351 (1999), no. 2, 735-780. https://doi.org/10.1090/S0002-9947-99-02168-6
- A. Weil, Sur certains groupes d'operateurs unitares, Acta Math. 111 (1964), 143-211 https://doi.org/10.1007/BF02391012
- A. Weil, Collected Papers (1964-1978), Vol. III, Springer-Verlag (1979), 1-69.
- J.-H. Yang, Harmonic analysis on the quotient spaces of Heisenberg groups, Nagoya Math. J. 123 (1991), 103-117.
- J.-H. Yang, Remarks on Jacobi forms of higher degree, Proc. of the 1993 Workshop on automorphic forms and related topics (Seoul, 1993), 33-58, Pyungsan Inst. Math. Sci., Seoul, 1993.
- J.-H. Yang, The Siegel-Jacobi Operator, Abh. Math. Sem. Univ. Hamburg 63 (1993), 135-146. https://doi.org/10.1007/BF02941338
- J.-H. Yang, Harmonic analysis on the quotient spaces of Heisenberg groups. II, J. Number Theory 49 (1994), no. 1, 63-72. https://doi.org/10.1006/jnth.1994.1080
- J.-H. Yang, Singular Jacobi forms, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2041-2049. https://doi.org/10.1090/S0002-9947-1995-1290733-2
- J.-H. Yang, Construction of vector valued modular forms from Jacobi forms, Canad. J. Math. 47 (1995), no. 6, 1329-1339. https://doi.org/10.4153/CJM-1995-068-2
- J.-H. Yang, A decomposition theorem on differential polynomials of theta functions of high level, Japan. J. Math. (N.S.) 22 (1996), no. 1, 37-49.
-
J.-H. Yang, Fock representations of the Heisenberg group
$H_{\mathbb{R}}^{(g,h)}$ , J. Korean Math. Soc. 34 (1997), no. 2, 345-370. - J.-H. Yang, Lattice representations of Heisenberg groups, Math. Ann. 317 (2000), no. 2, 309-323. https://doi.org/10.1007/s002080000097
- J.-H. Yang, A note on a fundamental domain for Siegel-Jacobi space, Houston J. Math. 32 (2006), no. 3, 701-712.
- J.-H. Yang, Invariant metrics and Laplacians on Siegel-Jacobi space, J. Number Theory 127 (2007), no. 1, 83-102. https://doi.org/10.1016/j.jnt.2006.12.014
- J.-H. Yang, A partial Cayley transform of Siegel-Jacobi disk, J. Korean Math. Soc. 45 (2008), no. 3, 781-794. https://doi.org/10.4134/JKMS.2008.45.3.781
- J.-H. Yang, Invariant metrics and Laplacians on Siegel-Jacobi disk, Chin. Ann. Math. Ser. B 31 (2010), no. 1, 85-100. https://doi.org/10.1007/s11401-008-0348-7
- J.-H. Yang, Heisenberg Group, Theta Functions and the Weil Representation, Kyung Moon Sa, Seoul, 2012.
- J.-H. Yang, A note on Maass-Jacobi forms II, Kyungpook Math. J. 53 (2013), no. 1, 49-86. https://doi.org/10.5666/KMJ.2013.53.1.49
- J.-H. Yang, Y.-H. Yong, S.-N. Huh, J.-H. Shin, and G.-H. Min, Sectional curvatures of the Siegel-Jacobi space, Bull. Korean Math. Soc. 50 (2013), no. 3, 787-799. https://doi.org/10.4134/BKMS.2013.50.3.787
- C. Ziegler, Jacobi forms of higher degree, Abh. Math. Sem. Univ. Hamburg 59 (1989), 191-224. https://doi.org/10.1007/BF02942329
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