Introduction to the Representation Theory of Compact and Locally Compact Groups (London Mathematical Society Lecture Note Series, Series Number 80)

Because Of Their Significance In Physics And Chemistry, Representation Of Lie Groups Has Been An Area Of Intensive Study By Physicists And Chemists, As Well As Mathematicians. This Introduction Is Designed For Graduate Students Who Have Some Knowledge Of Finite Groups And General Topology, But Is Otherwise Self-contained. The Author Gives Direct And Concise Proofs Of All Results Yet Avoids The Heavy Machinery Of Functional Analysis. Moreover, Representative Examples Are Treated In Some Detail. Alain Robert. Includes Index. CONTENTS......Page 5 Foreword......Page 7 Conventional notations and terminology......Page 9 PART I : REPRESENTATIONS OF COMPACT GROUPS......Page 11 1. Compact groups and Haar measures p.......Page 13 Exercises......Page 21 2. Representations, general constructions......Page 23 Exercises......Page 30 3. A geometrical application......Page 31 Exercises......Page 38 4. Finite-dimensional representations of compact groups......Page 39 (Peter-Weyl theorem)......Page 48 5. Decomposition of the regular representation......Page 50 Exercises......Page 61 6. Convolution, Plancherel formula & Fourier inversion......Page 63 Exercises......Page 71 7. Characters and group algebras......Page 73 Exercises......Page 86 8. Induced representations and Frobenius-1Veil reciprocity......Page 88 Exercises......Page 99 9. Tannaka duality......Page 100 10. Representations of the rotation group......Page 105 Exercises......Page 117 PART II : REPRESENTATIONS OF LOCALLY COMPACT GROUPS......Page 119 11. Groups with few finite-dimensional representations......Page 121 Exercises......Page 126 12. Invariant measures on locally compact groups and homogeneous spaces......Page 127 Exercises......Page 136 13. Continuity properties of representations......Page 138 14. Representations of G and of L'(G)......Page 143 Exercises......Page 154 15. Schur's lemma : unbounded version......Page 155 Exercises......Page 160 16. Discrete series of locally compact groups......Page 161 Exercises......Page 172 17. The discrete series of S 12 (JR)......Page 174 Exercises......Page 181 18. The principal series of S12OR)......Page 182 19. Decomposition along a commutative subgroup......Page 189 Appendix: Note on Hilbertian integrals......Page 195 20. Type I groups......Page 197 Exercises......Page 203 21. Getting near an abstract Plancherel formula......Page 204 Epilogue......Page 211 References......Page 212 Index......Page 214