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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction...................................................................................................... 5
Chapter I. Invariant kernels on locally compact groups and cyclic
representations....................................................................................................... 8
1. Distributions on topological groups.......................................... 8
2. Invariant kernels and cyclic representations.................................... 9
3. Generalized cyclic vectors. An extension of the Gelfand-Raikov
correspondence......................................................................................... 12
4. Cyclicity of induced representations.................................................. 15
Chapter II. Duality theorems for induced representations
with elliptic differential operator............................................................................. 17
1. Induced representations............................................................... 17
2. Invariant differential operators.............................................................. 19
3. The general duality theorem for induced representations.............. 20
4. Duality theorems with elliptic differential operator............................ 22
5. The case where G/Γ is not compact.................................................... 30
Chapter III. The duality theorem and Langlands conjectures................. 30
1. The discrete series representations........................................... 31
2. The Langlands conjectures.................................................................. 32
Chapter IV. Dirac operator and the discrete classes.
Hotta and Parthasarathy theorem......................................................................... 30
1. Dirac operator.................................................................................. 39
2. The realization of the discrete series representations.................... 42
3. The multiplicity theorem......................................................................... 45
References........................................................................................................ 46
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
168
Liczba stron
48
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXVIII
Daty
wydano
1980
Twórcy
autor
Bibliografia
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- [13] Ph. Griffiths and W. Schmid, Locally homogeneous complex manifolds, Acta Math. 123 (1969), pp. 253-302.
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- [16] H. Hecht and W. Schmid, The proof of Blattner's conjecture, Inv. Math. 31 (1975), pp. 129-154.
- [17] R. Hotta and R. Parthasarathy, A geometric meaning of the multiplicity of integrable discrete classes in $L^2$(Γ\G), Ossaka J. Math. 10 (1973), p. 211-234.
- [18] R. Hotta, Multiplicity formulae for discrete series, Inv. Math. 26 (1974), pp. 133-178.
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- [21] R. Langlands, Dimension of spaces of automorphic forms, In: Proc. Symp. Pure Math., Vol. IX (1966), Algebraic groups and discontinuous subgroups, pp. 253-267.
- [22] K. Maurin, Distributionen auf Tamabe-Groupen. Harmonische Analyse auf einer Abelschen l.k. Groupen, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astr. Phys. 9 (1961), pp. 846-850.
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- [24] K. Maurin and L. Maurin, A generalization of the duality theorem of Gelfand-Piateckii-Šapiro and Tamagava automorphic forms, J. Fac. Sci. Univ. Tokyo 17 (1970), pp. 331-339.
- [25] K. Maurin, General duality theorem for automorphic forms and reciprocity theorem of Frobenius-Bruhat type. Preprint no. 25 (1971). Polish Academy of Sciences.
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- [28] D. Montgomery and L. Zippin, Topological transformations groups, New York 1956.
- [29] M. S. Narasimhan and K. Okamato, An analogue of the Borel-Weil-Bott theorem for hermitian symmetric pairs of non-compact type, Ann. of Math. 91 (1970), pp. 486-511.
- [30] R. Panney, Abstract Plancherel theorems and a Frobenius reciprocity theorem, J. Funct. Anal. 18 (1975), pp. 177-184.
- [31] R. Parthasarathy, Dirac operator and the discrete series, Ann. of Math. 96 (1972), pp. 1-30.
- [32] N. Skovhus Poulsen, On $C^∞$-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal. 9 (1972), pp. 87-120.
- [33] W. Schmid, On a conjecture of Langlands, Ann. of Math. 93 (1971), pp. 1-42.
- [34] W. Schmid, On the characters of the discrete series. The hermitian symmetric case, Inv. Math. 30 (1975), pp. 47-144.
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- [35] L. Schwartz, Complex analytic manifolds. Elliptic partial differential equations (Russian), Moscow 1964.
- [36] J. Szmidt, Invariant kernels on locally compact groups and cyclic representations, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astr. Phys. 23 (1975), pp. 1073-1078.
- [37] J. Szmidt and A. Wawrzyńczyk, On $C^∞$-vectors and intertwining operators for Banach space representations of Lie groups, Preprint no. 61 (1973), Polish Academy of Sciences, and Bull. Acad, Polon. Sci., Ser. Sci. Math. Astr. Phys. 22 (1974), pp. 513-520.
- [38] P. C. Trambi and V. S. Varadarajan, Asymptotic behaviour of eigenfunctions on a semisimple Lie group: the discrete spectrum, Acta Math. 129 (1972), pp. 237-280.
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- [40] G. Warner, Harmonic analysis on semisimple Lie groups I, II, Springer-Verlag, 1972.
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