Unitary Representations and Unitary Duals
This graduate textbook introduces the unitary representation theory of groups, emphasizing applications in fields like dynamical systems. It begins with the general theory and motivation, then explores key classes of groups. Abelian and compact groups are treated through Pontryagin duality and the P...
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
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Springer Nature Switzerland : Imprint: Springer,
2025.
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| Ausgabe: | 1st ed. 2025. |
| Schriftenreihe: | Graduate Texts in Mathematics,
308 |
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| Online-Zugang: | https://doi.org/10.1007/978-3-032-03899-9 |
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| 100 | 1 | |a Einsiedler, Manfred. |e author. |0 (orcid)0009-0001-2372-5894 |1 https://orcid.org/0009-0001-2372-5894 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 0 | |a Unitary Representations and Unitary Duals |h [electronic resource] / |c by Manfred Einsiedler, Thomas Ward. |
| 250 | |a 1st ed. 2025. | ||
| 264 | 1 | |a Cham : |b Springer Nature Switzerland : |b Imprint: Springer, |c 2025. | |
| 300 | |a 1 online resource (XVII, 564 p. 27 illus.). | ||
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| 341 | 0 | |b Table of contents navigation |2 onix | |
| 341 | 0 | |b Single logical reading order |2 onix | |
| 341 | 0 | |b Short alternative textual descriptions |2 onix | |
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| 341 | 0 | |b Use of high contrast between text and background colour |2 onix | |
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| 490 | 1 | |a Graduate Texts in Mathematics, |x 2197-5612 ; |v 308 | |
| 505 | 0 | |a 1 Unitary Representations -- 2 Abelian Groups -- 3 Compact Groups -- 4 Lie Algebras and Unitary Representations of SU2(R) -- 5 Normal Abelian Subgroups and Unitary Duals -- 6 Weak Containment and the Fell Topology -- 7 Smooth Vectors and Decay for SL3(R) -- 8 Discrete Series Representations and Temperedness -- 9 Unitary Representations of SL2(R) -- Appendix A: Linear Algebra -- Appendix B: Analysis -- Appendix C: Topological Groups. | |
| 520 | |a This graduate textbook introduces the unitary representation theory of groups, emphasizing applications in fields like dynamical systems. It begins with the general theory and motivation, then explores key classes of groups. Abelian and compact groups are treated through Pontryagin duality and the Peter–Weyl theorem. Metabelian groups illustrate links to ergodic theory and lead to the Mackey machine. Weak containment and the Fell topology are introduced through examples. The final chapters apply the theory to special linear groups in dimensions two and three, covering smooth vectors, spectral gaps, and decay of matrix coefficients. The two-dimensional case is examined in depth, including the Kunze–Stein phenomenon, spectral decomposition on the hyperbolic plane, and the Weil representation. The book concludes with a full description of the unitary dual of SL(2,R) and its Fell topology, applying the theory to prove effective equidistribution of horocycle orbits. With its focus on key examples and concrete explanations, this textbook is aimed at graduate students taking first steps in unitary representation theory. It builds the theory from the ground up, requiring only some familiarity with functional analysis beyond standard undergraduate mathematics. | ||
| 532 | 8 | |a Accessibility summary: This PDF does Not fully comply with PDF/UA standards but does include limited screen reader support, descriptions for Non-text content (such as images and graphs), bookmarks for easy navigation, and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognise the importance of accessibility and welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us via https://www.springernature.com/gp/info/accessibility | |
| 532 | 8 | |a Inaccessible, or known limited accessibility | |
| 532 | 8 | |a No reading system accessibility options actively disabled | |
| 532 | 8 | |a Publisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 588 | |a Print version record. | ||
| 650 | 0 | |a Topological groups. | |
| 650 | 0 | |a Lie groups. | |
| 650 | 0 | |a Harmonic analysis. | |
| 650 | 0 | |a Dynamical systems. | |
| 650 | 0 | |a Functional analysis. | |
| 650 | 1 | 4 | |a Topological Groups and Lie Groups. |
| 650 | 2 | 4 | |a Abstract Harmonic Analysis. |
| 650 | 2 | 4 | |a Dynamical Systems. |
| 650 | 2 | 4 | |a Functional Analysis. |
| 700 | 1 | |a Ward, Thomas. |e author. |0 (orcid)0000-0002-8253-5767 |1 https://orcid.org/0000-0002-8253-5767 |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
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| 776 | 0 | 8 | |i Printed edition: |z 9783032038982 |
| 776 | 0 | 8 | |i Printed edition: |z 9783032039002 |
| 830 | 0 | |a Graduate Texts in Mathematics, |x 2197-5612 ; |v 308 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/978-3-032-03899-9 |
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||
| 950 | |a Focus Bundle Mathematics and Statistics (SpringerNature-85421) | ||