The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ write by Toshiyuki Kobayashi. This book was released on 2011. The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$ available in PDF, EPUB and Kindle. The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.
The Schrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p, Q)
The Schrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p, Q) - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Schrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p, Q) write by Toshiyuki Kobayashi. This book was released on 2011. The Schrödinger Model for the Minimal Representation of the Indefinite Orthogonal Group O(p, Q) available in PDF, EPUB and Kindle.
Quantum Theory, Groups and Representations
Quantum Theory, Groups and Representations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Theory, Groups and Representations write by Peter Woit. This book was released on 2017-11-01. Quantum Theory, Groups and Representations available in PDF, EPUB and Kindle. This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.
An Introduction to Lie Groups and Lie Algebras
An Introduction to Lie Groups and Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Lie Groups and Lie Algebras write by Alexander A. Kirillov. This book was released on 2008-07-31. An Introduction to Lie Groups and Lie Algebras available in PDF, EPUB and Kindle. This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
A Journey Through Representation Theory
A Journey Through Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Journey Through Representation Theory write by Caroline Gruson. This book was released on 2018-10-23. A Journey Through Representation Theory available in PDF, EPUB and Kindle. This text covers a variety of topics in representation theory and is intended for graduate students and more advanced researchers who are interested in the field. The book begins with classical representation theory of finite groups over complex numbers and ends with results on representation theory of quivers. The text includes in particular infinite-dimensional unitary representations for abelian groups, Heisenberg groups and SL(2), and representation theory of finite-dimensional algebras. The last chapter is devoted to some applications of quivers, including Harish-Chandra modules for SL(2). Ample examples are provided and some are revisited with a different approach when new methods are introduced, leading to deeper results. Exercises are spread throughout each chapter. Prerequisites include an advanced course in linear algebra that covers Jordan normal forms and tensor products as well as basic results on groups and rings.
