During the past two decades, Roger Penrose's twistor theory has been a continuing source of mathematical inspiration. This ambitious theory aims to reformulate the foundations of physics using conformal and complex geometry. At the heart of twistor theory lies a geometrical transform know as the Penrose transform. This book provides coverage of this transform in a general setting, utilizing complex homogeneous spaces, with mathematical input taken from the representation theory of Lie groups. The Penrose Transform gives readers much original research that is not available in any other text, with special attention to the twistor theory of Minkowski space.

Product Description: This book discusses the representation theory of symmetric groups, the theory of symmetric functions and the polynomial representation theory of general linear groups. The first chapter provides a detailed account of necessary representation-theoretic background...read more

Product Description: Representation theory is an important part of modern mathematics, not only as a subject in its own right but also as a tool for many applications. It provides a means for exploiting symmetry, making it particularly useful in number theory, algebraic geometry, and differential geometry, as well as classical and modern physics...read more

Written by one of the world's leading algebraic topologists, this book introduces new techniques from topology into algebra, addressing several topics in algebra which are unified by their connection with the representation theory of Galois groups. Treatment is self-contained, addressing bilinear forms and local root numbers using techniques from cohomology theory, homotopy, and stable homotopy theory. Snaith's innovative approach is likely to inspire many similar applications of the explicit Brauer induction theory. Contains much original research of interest to algebraic topologists, number theorists, and group theorists.

Product Description: A "$2$-group" is a category equipped with a multiplication satisfying laws like those of a group. Just as groups have representations on vector spaces, $2$-groups have representations on "$2$-vector spaces", which are categories analogous to vector spaces...read more

Product Description: This graduate-level textbook provides an elementary exposition of the theory of automorphic representations and L-functions for the general linear group in an adelic setting. Definitions are kept to a minimum and repeated when reintroduced so that the book is accessible from any entry point, and with no prior knowledge of representation theory...read more

Product Description: This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators such as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces...read more

Product Description: Deligne-Lusztig theory aims to study representations of finite reductive groups by means of geometric methods, and particularly l-adic cohomology. Many excellent texts present, with different goals and perspectives, this theory in the general setting...read more

Product Description: This volume offers a thorough study of symmetric algebras, covering topics such as block theory, representation theory and Clifford theory. It can also serve as an introduction to the Hecke algebras of complex reflection groups.

Product Description: First published in 1962, this classic book remains a remarkably complete introduction to various aspects of the representation theory of finite groups. One of its main advantages is that the authors went far beyond the standard elementary representation theory, including a masterly treatment of topics such as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations...read more

Product Description: The Description for this book, Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups. (AM-94), will be forthcoming.