This book is directed primarily at undergraduate and postgraduate students interested to get acquainted with the representation theory of Lie algebras. The book treats the case of the smallest simple Lie algebra, namely, the Lie algebra sl_2. It contains classical contents including the description of all finite-dimensional modules and an introduction to the universal enveloping algebras with its primitive ideals, alongside non-classical contents including the description of all simple weight modules, the category of all weight modules, a detailed description of the category O, and especially, a description of all simple modules. The book also contains an account of a new research direction: the categorification of simple finite-dimensional modules./a

Concise book offers expository account of theory of modular forms and its application to number theory and analysis. Substantial notes at the end of each chapter amplify the more difficult subjects. 1969 edition.

This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables and Hilbert modular surfaces. The third series gives an introduction to Siegel modular forms and discusses a conjecture by Harder. It also contains Harder's original manuscript with the conjecture. Each part treats a number of beautiful applications.

Paths to College and Career Jossey-Bass and PCG Education are proud to bring the Paths to College and Career English Language Arts (ELA) curriculum and professional development resources for grades 6–12 to educators across the country. Originally developed for EngageNY and written with a focus on the shifts in instructional practice and student experiences the standards require, Paths to College and Career includes daily lesson plans, guiding questions, recommended texts, scaffolding strategies and other classroom resources. Paths to College and Career is a concrete and practical ELA instructional program that engages students with compelling and complex texts. At each grade level, Paths to College and Career delivers a yearlong curriculum that develops all students' ability to read closely and engage in text-based discussions, build evidence-based claims and arguments, conduct research and write from sources, and expand their academic vocabulary. Paths to College and Career's instructional resources address the needs of all learners, including students with disabilities, English language learners, and gifted and talented students. This enhanced curriculum provides teachers with freshly designed Teacher Guides that make the curriculum more accessible and flexible, a Teacher Resource Book for each module that includes all of the materials educators need to manage instruction, and Student Journals that give students learning tools for each module and a single place to organize and document their learning. As the creators of the Paths ELA curriculum for grades 6–12, PCG Education provides a professional learning program that ensures the success of the curriculum. The program includes: Nationally recognized professional development from an organization that has been immersed in the new standards since their inception. Blended learning experiences for teachers and leaders that enrich and extend the learning. A train-the-trainer program that builds capacity and provides resources and individual support for embedded leaders and coaches. Paths offers schools and districts a unique approach to ensuring college and career readiness for all students, providing state-of-the-art curriculum and state-of-the-art implementation.

Paths to College and Career Jossey-Bass and PCG Education are proud to bring the Paths to College and Career English Language Arts (ELA) curriculum and professional development resources for grades 6–12 to educators across the country. Originally developed for EngageNY and written with a focus on the shifts in instructional practice and student experiences the standards require, Paths to College and Career includes daily lesson plans, guiding questions, recommended texts, scaffolding strategies and other classroom resources. Paths to College and Career is a concrete and practical ELA instructional program that engages students with compelling and complex texts. At each grade level, Paths to College and Career delivers a yearlong curriculum that develops all students' ability to read closely and engage in text-based discussions, build evidence-based claims and arguments, conduct research and write from sources, and expand their academic vocabulary. Paths to College and Career's instructional resources address the needs of all learners, including students with disabilities, English language learners, and gifted and talented students. This enhanced curriculum provides teachers with freshly designed Teacher Guides that make the curriculum more accessible and flexible, a Teacher Resource Book for each module that includes all of the materials educators need to manage instruction, and Student Journals that give students learning tools for each module and a single place to organize and document their learning. As the creators of the Paths ELA curriculum for grades 6–12, PCG Education provides a professional learning program that ensures the success of the curriculum. The program includes: Nationally recognized professional development from an organization that has been immersed in the new standards since their inception. Blended learning experiences for teachers and leaders that enrich and extend the learning. A train-the-trainer program that builds capacity and provides resources and individual support for embedded leaders and coaches. Paths offers schools and districts a unique approach to ensuring college and career readiness for all students, providing state-of-the-art curriculum and state-of-the-art implementation.

This text is devoted to mathematical structures arising in conformal field theory and the q-deformations. The authors give a self-contained exposition of the theory of Knizhnik-Zamolodchikov equations and related topics. No previous knowledge of physics is required. The text is suitable for a one-semester graduate course and is intended for graduate students and research mathematicians interested in mathematical physics.

The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and “fun” subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin–Lehner–Li theory of newforms and including the theory of Eisenstein series, Rankin–Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacobi, Maass, and Siegel modular forms. Some “gems” of the book are an immediately implementable trace formula for Hecke operators, generalizations of Haberland's formulas for the computation of Petersson inner products, W. Li's little-known theorem on the diagonalization of the full space of modular forms, and explicit algorithms due to the second author for computing Maass forms. This book is essentially self-contained, the necessary tools such as gamma and Bessel functions, Bernoulli numbers, and so on being given in a separate chapter.

Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions