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The duality theorems. Cyclic representations Langlands conjectures

100%

Szmidt J.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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Congruences among generalized Bernoulli numbers

49%

Szmidt J., Urbanowicz J., Zagier D.

Acta Arithmetica

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1995

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tom 71

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nr 3

273-278

3

The Selberg trace formula for the Picard group SL(2, Z[i])

31%

Szmidt J.

Acta Arithmetica

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1982-1983

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tom 42

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nr 4

391-424

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Nonlinearity of the round function

25%

Kontak M., Szmidt J.

Control and Cybernetics

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2007

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tom 36

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nr 4

1037-1044

Ograniczanie wyników

2 Acta Arithmetica

1 Control and Cybernetics

4 Szmidt J.

1 Kontak M.

1 Urbanowicz J.

1 Zagier D.

1 2007

1 1995

1 1983

1 1980

The duality theorems. Cyclic representations Langlands conjectures

Congruences among generalized Bernoulli numbers

The Selberg trace formula for the Picard group SL(2, Z[i])

Nonlinearity of the round function