Last edited by Shakatilar

Thursday, July 16, 2020 | History

2 edition of **Unitary representations of solvable lie groups** found in the catalog.

Unitary representations of solvable lie groups

Louis Auslander

- 392 Want to read
- 38 Currently reading

Published
**1966**
by American Mathematical Society in Providence
.

Written in English

- Lie groups.

**Edition Notes**

Statement | by Louis Auslander and Calvin C. Moore. |

Series | American Mathematical Society. Memoirs -- no. 62., Memoirs of the American Mathematical Society -- no. 62. |

Contributions | Moore, C. C. 1936- |

The Physical Object | |
---|---|

Pagination | 199 p. |

Number of Pages | 199 |

ID Numbers | |

Open Library | OL17769653M |

The present book is devoted to lattices, i.e. discrete subgroups of finite covolume, in semi-simple Lie groups. By "Lie groups" we not only mean real Lie groups, but also the sets of k-rational points of algebraic groups over local fields k and their direct products. Our results can be applied to the theory of algebraic groups over global fields. Unitary Representations. The more classical and familiar side of the subject is the study of unitary representations of Lie groups (on Hilbert space H). Such a representation has an enveloping algebra of unbounded operators on H, and it is obtained by differentiation of the given unitary representation along the Lie : Dover Publications.

notably the reference book [G80]. that unitary representations with non-vanishing 1-cohomology for a given group are rare. For instance, it is an easy observation of Guichardet [G72] that if G is ing connected solvable Lie groups, algebraic solvable p-adic groups, and ﬁnitely generated solvable groups with ﬁnite Pru¨fer rank. Some uncertainty principles for diamond Lie groups; Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators; Topology on the unitary dual of completely solvable Lie groups; Rayleigh theorem, projection of orbital measures and spline functionsAuthor: Detlev Poguntke.

Remark. Such a result finds an analogue in the mathematical literature in a theorem due to V. Bargmann, published in his paper "On Unitary Ray Representations of Continuous Groups" (), (PDF via JSTOR).A simplified proof of Bargmann's theorem was later given by D. J. Simms (), see Ch.2 of his monograph "Lie Groups and Quantum Mechanics" (Springer-link). For type I groups G (which include the real reductive Lie groups), there is a bijection between irreducible unitary representations of G and primitive ideals in C*(G). Now this bijection is a powerful technical tool for example, it is at the heart of the abstract theory of decomposition into irreducible by:

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Additional Physical Format: Online version: Auslander, Louis. Unitary representations of solvable Lie groups. Providence, R.I.: American Mathematical Society, Additional Physical Format: Online version: Brezin, Jonathan Paul, Unitary representation theory for solvable lie groups.

Providence, American Mathematical Society, []. A Lie algebra Unitary representations of solvable lie groups book called completely solvable or split solvable if it has an elementary sequence{(V) As above definition} of ideals in from to.

A finite-dimensional nilpotent Lie algebra is completely solvable, and a completely solvable Lie algebra is solvable. Unitary representations of solvable Lie groups, (Memoirs of the American Mathematical Society) [Auslander, Louis] on *FREE* shipping on qualifying offers.

Unitary representations of solvable Lie groups, (Memoirs of the American Mathematical Society)Author: Louis Auslander. Lie groups are smooth differentiable manifolds and as such can be studied using differential calculus, in contrast with the case of more general topological of the key ideas in the theory of Lie groups is to replace the global object, the group, with its local or linearized version, which Lie himself called its "infinitesimal group" and which has since become known as its Lie.

This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field.

As well, various related topics are presented to motivate young orbit method invented by Kirillov is applied. Unitary repns of non-compact non-abelian Lie groups tend to be infinite-dimensional. There is a divergence between two extreme types: nilpotent versus reductive (or semi-simple).

Nilpotent (or solvable) Lie groups don't have very interesting compact subgroups. Reductive or semi-simple ones, like SL(2,R), do have. Buy Harmonic Analysis on Exponential Solvable Lie Groups (Springer Monographs in Mathematics) on FREE SHIPPING on qualified ordersCited by: The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups.

This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained.

Leptin, Horst / Ludwig, Jean Unitary Representation Theory of Exponential Lie Groups. Unitary Representation Theory for Solvable Lie Groups Unitary Representation Theory for Solvable Lie Groups. @: 温馨提示：本站免费提供疑难偏英文书查找服务: 相关英文书. Linear Representations of Finite Groups.

$\begingroup$ Yemon, His formula is very precise and very explicit unlike most Plancherel formulas for Nilpotent Lie groups available in the Literature.

Another resource if you want would be "Representations of nilpotent Lie groups and their applications" a book written by Corwin and Greenleaf. Vignon S. Oussa $\endgroup$ – Vignon Mar 10 ' Rossi, H., Vergne, M.: Representations of certain solvable Lie groups on Hilbert spaces of holomorphic functions and the application to the holomorphic discrete series of Author: Hidenori Fujiwara, Jean Ludwig.

Author(s): Representations of Solvable Lie Groups: Basic Theory and Examples (New Mathematical Monographs Book. Ghas enough irreducible unitary representations to separate the points of G, trig-gering a systematic study of unitary representations for such groups.

First ma-jor results on classiﬁcations of unitary duals did concern the aﬃne group Aﬀ(R) of R [GeNa–47a], the special linear group SL(2,C) [GeNa–47b], and SL(2,R) [Barg–47].Author: Bachir Bekka, Pierre de la Harpe.

Abdelmoula, L., Arnal, D., Selmi, M.: Separation of unitary representations of Type I solvable Lie groups of the form R × R d. Lie The – () Graduate Texts in Mathematics Book. BIOGRAPHY After Tufts, I spent four and a half years aboard ships as an officer in the U.S.

Navy. Then after quickly filling in a gap of several mathematics courses that I missed as an undergraduate non-mathmematics major, I began a Ph.D.

program at Berkeley and finished with a thesis on unitary representations of solvable Lie : @ Kostant and Kirillov initiated an orbit method of classifying the irreducible unitary representations of simply-connected solvable Lie groups.

This was a generalization of the Borel-Weil theorem to certain classes of noncompact groups. All attempts to generalize this method to arbitrary groups, however, have Size: KB.

There is a book titled "Group theory and Physics" by Sternberg that covers the basics, including crystal groups, Lie groups, representations. I think it's a good introduction to the topic.

To quote a review on Amazon (albeit the only one): "This book is an excellent introduction to the use of group theory in physics, especially in crystallography, special relativity and particle physics.

Convexity and unitary representations of nilpotent Lie groups. of a larger solvable group G(+), and we extend the representation from G to G+, in such a Author: Norman Wildberger. Para>Let us consider holomorphically induced representations for an exponential solvable Lie group [equation].

Since the stabilizer G(f) in G of any Author: Hidenori Fujiwara, Jean Ludwig. This book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups.

There still are many interesting open problems, and the book contributes to the future progress of this research : Springer Japan.Many years ago I wrote the book Lie Groups, Lie Algebras, and Some of Their Applications (NY: Wiley, ).

That was a big book: long and diﬃcult. Over the course of the years I realized that more than 90% of the most useful material in that book could be presented in less than 10% of the space. This realization was accompanied by a promiseFile Size: KB.