Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-25T16:24:15.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Poisson transforms and mixed automorphic forms on semisimple Lie groups

Published online by Cambridge University Press:  17 April 2009

Min Ho Lee  and
Hyo Chul Myung
Min Ho Lee
Affiliation:
Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, United States of America, e-mail: lee@math.uni.edu
Hyo Chul Myung
Affiliation:
Korea Institute for Advanced Study and KAIST, 207-43 Chunryangri-dong, Dongdaemoon-ku, Seoul 130-012, Korea, e-mail: hm@kias.re.kr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We discuss Poisson transforms which carry sections of certain vector bundles to mixed automorphic forms, and identify vector bundles whose sections are liftings of holomorphic forms on families of Abelian varieties via Poisson transforms.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 3 , June 2000 , pp. 353 - 370
Copyright
Copyright © Australian Mathematical Society 2000

References

REFERENCES

[1]Baily, W. and Borel, A., ‘Compactification of arithmetic quotients of bounded symmetric domains, Ann. of Math. 84 (1966), 442–528.CrossRefGoogle Scholar
[2]Borel, A., ‘Introduction to automorphic forms’, in Algebraic Groups and Discontinuous Subgroups, Boulder, Colo. 1965, Proc. Sympos. Pure Math. 9 (Amer. Math. Soc., Providence, R.I., 1966), pp. 199–210.Google Scholar
[3]Helgason, S., Geometric analysis on symmetric spaces (Amer. Math. Soc., Providence, R.I., 1994).Google Scholar
[4]Hunt, B. and Meyer, W., ‘Mixed automorphic forms and invariants of elliptic surfaces, Math. Ann. 271 (1985), 53–80.CrossRefGoogle Scholar
[5]Knapp, A., Representation theory of semisimple groups: An overview based on examples (Princeton University Press, Princeton, 1986).CrossRefGoogle Scholar
[6]Kuga, M., Fiber varieties over a symmetric space whose fibers are abelian varieties I, II (Univ. of Chicago, Chicago, 1963/1964).Google Scholar
[7]Lee, M.H., ‘Mixed cusp forms and holomorphic forms on elliptic varieties, Pacific J. Math. 132 (1988), 363–370.CrossRefGoogle Scholar
[8]Lee, M. H., ‘Mixed Siegel modular forms and Kuga fiber varieties, Illinois J. Math. 38 (1994), 692–700.CrossRefGoogle Scholar
[9]Lee, M. H., ‘Mixed automorphic forms on semisimple Lie groups, Illinois J. Math. 40 (1966), 464–478.Google Scholar
[10]Lee, M. H., ‘Mixed automorphic vector bundles on Shimura varieties, Pacific J. Math. 173 (1996), 105–126.CrossRefGoogle Scholar
[11]Lee, M. H., ‘Mixed Hilbert modular forms and families of abelian varieties, Glasgow Math. J. 39 (1997), 131–140.CrossRefGoogle Scholar
[12]Minemura, K., ‘Invariant differential operators and spherical sections on a homogeneous vector bundle, Tokyo J. Math. 15 (1992), 231–245.CrossRefGoogle Scholar
[13]Mumford, D., ‘Families of abelian varieties’, in Algebraic Groups and Discontinuous Subgroups, Boulde, Colo. 1965, Proc. Sympos. Pure Math. 9 (Amer. Math. Soc., Providence, R.I., 1966), pp. 347–351.CrossRefGoogle Scholar
[14]Murakami, S., Cohomology of vector-valued forms on symmetric spaces (Univ. of Chicago, Chicago, 1966).Google Scholar
[15]Rudin, W., Real and complex analysis, (Third edition) (McGraw-Hill, New York, 1987).Google Scholar
[16]Satake, I., Algebraic structures of symmetric domains (Princeton Univ. Press, Princeton, 1980).Google Scholar
[17]Wallach, N., Harmonic analysis in homogeneous spaces (Marcel Dekker, New York, 1973).Google Scholar