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INVARIANT DIFFERENTIAL OPERATORS ON THE MINKOWSKI-EUCLID SPACE
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 Title & Authors
INVARIANT DIFFERENTIAL OPERATORS ON THE MINKOWSKI-EUCLID SPACE
Yang, Jae-Hyun;
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 Abstract
For two positive integers and , let be the open convex cone in consisting of positive definite real symmetric matrices and let be the set of all real matrices. In this paper, we investigate differential operators on the non-reductive homogeneous space that are invariant under the natural action of the semidirect product group on the Minkowski-Euclid space . These invariant differential operators play an important role in the theory of automorphic forms on generalizing that of automorphic forms on .
 Keywords
invariants;invariant differential operators;the Minkowski-Euclid space;
 Language
English
 Cited by
1.
POLARIZED REAL TORI,;

대한수학회지, 2015. vol.52. 2, pp.269-331 crossref(new window)
 References
1.
Harish-Chandra, Representations of semisimple Lie groups. I, Trans. Amer. Math. Soc. 75 (1953), 185-243. crossref(new window)

2.
Harish-Chandra , The characters of semisimple Lie groups, Trans. Amer. Math. Soc. 83 (1956), 98-163. crossref(new window)

3.
S. Helgason, Differential operators on homogeneous spaces, Acta Math. 102 (1959), 239-299. crossref(new window)

4.
S. Helgason, Groups and Geometric Analysis, Academic Press, New York, 1984.

5.
R. Howe, Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond, The Schur lectures (1992) (Tel Aviv), 1-82, Israel Math. Conf. Proc., 8, Bar-Ilan Univ., Ramat Gan, 1995.

6.
M. Itoh, On the Yang Problem (SFT), Max-Planck Institut f¨ur Mathematik, Bonn, 2011.

7.
H. Maass, Die Bestimmung der Dirichletreihnen mit Grossencharakteren zu den Modulformen n-ten Grades, J. Indian Math. Soc. 9 (1955), 1-23.

8.
H. Maass, Siegel modular forms and Dirichlet series, Lecture Notes in Math., vol. 216, Springer-Verlag, Berlin-Heidelberg-New York, 1971.

9.
H. Minkowski, Gesammelte Abhandlungen, Chelsea, New York, 1967.

10.
A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. B. 20 (1956), 47-87.

11.
A. Terras, Harmonic Analysis on Symmetric Spaces and Applications II, Springer- Verlag, 1988.

12.
H. Weyl, The classical groups: Their invariants and representations, Princeton Univ. Press, Princeton, New Jersey, second edition, 1946.

13.
J.-H. Yang, Singular Jacobi forms, Trans. Amer. Math. Soc. 347 (1995), no. 6, 2041- 2049. crossref(new window)

14.
J.-H. Yang, Polarized Real Tori, arXiv:0912.5084v1 [math.AG] (2009) or a revised version (2012).