Published annually, this comprehensive study guide for the Certified Public Accountant's (CPA) Exam arms readers with detailed outlines and study guidelines, plus skill-building problems and solutions that help them to master the topics that need the most work. With timely, up-to-the-minute coverage for the computerized CPA Exam, Wiley CPA Exam Review 2009: Financial Accounting and Reporting covers all current AICPA content requirements in financial accounting as well as new financial accounting standards. CPA candidates will find everything they need in order to pass the new computerized CPA Examination.

Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics, Series Number 55)

Computers & Technology

Bump, Daniel

Software

Cambridge University Press

This book covers both the classical and representation theoretic views of automorphic forms in a style that is accessible to graduate students entering the field. The treatment is based on complete proofs, which reveal the uniqueness principles underlying the basic constructions. The book features extensive foundational material on the representation theory of GL(1) and GL(2) over local fields, the theory of automorphic representations, L-functions and advanced topics such as the Langlands conjectures, the Weil representation, the Rankin-Selberg method and the triple L-function, and examines this subject matter from many different and complementary viewpoints. Researchers as well as students in algebra and number theory will find this a valuable guide to a notoriously difficult subject.

Science & Math

Mathematics

Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics.These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished.The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.

Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175) (Annals of Mathematics Studies)

Friedberg, Solomon

Brubaker, Ben

Oxford University Press

This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition.
For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.

Lie Groups (Graduate Texts in Mathematics, 225)

Springer

Going beyond the representation theory of compact Lie groups, this book offers a carefully chosen range of material conveying the bigger picture. Covers Lie algebra, Weyl character formula, symmetrical function theory, Satake diagrams, Sage software and more.

Algebraic Geometry

World Scientific Publishing Co Pte Ltd

This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

CRYSTAL BASES: REPRESENTATIONS AND COMBINATORICS

Schilling, Anne

World Scientific Publishing Company

"The introduction to crystal bases given in this book is accessible to graduate students and researchers. Its combinatorial approach is reader-friendly and invites the reader to get involved, either working on the exercises listed at the end of each chapter or by playing with the computational implementation on freely-available software, sage in this case, where the authors have many built-in accessible examples and some algorithms for specific crystal bases." MAA Reviews This unique book provides the first introduction to crystal base theory from the combinatorial point of view. Crystal base theory was developed by Kashiwara and Lusztig from the perspective of quantum groups. Its power comes from the fact that it addresses many questions in representation theory and mathematical physics by combinatorial means. This book approaches the subject directly from combinatorics, building crystals through local axioms (based on ideas by Stembridge) and virtual crystals. It also emphasizes parallels between the representation theory of the symmetric and general linear groups and phenomena in combinatorics. The combinatorial approach is linked to representation theory through the analysis of Demazure crystals. The relationship of crystals to tropical geometry is also explained.

Crystal Bases: Representations And Combinatorics

WSPC

See the best price to sell, buy, or rent books by Bump, Daniel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Bump, Daniel

See the best price to sell, buy, or rent books by Bump, Daniel. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics, Series Number 55)

Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics, Series Number 55)

Automorphic Forms and Representations (Cambridge Studies in Advanced Mathematics, Series Number 55)

Weyl Group Multiple Dirichlet Series: Type A Combinatorial Theory (AM-175) (Annals of Mathematics Studies)

Lie Groups (Graduate Texts in Mathematics, 225)

Lie Groups (Graduate Texts in Mathematics, 225)

Algebraic Geometry

CRYSTAL BASES: REPRESENTATIONS AND COMBINATORICS

Crystal Bases: Representations And Combinatorics