| eBook ISBN: | 978-0-8218-8236-8 |
| Product Code: | CONM/557.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| eBook ISBN: | 978-0-8218-8236-8 |
| Product Code: | CONM/557.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
-
Book DetailsContemporary MathematicsVolume: 557; 2011; 388 ppMSC: Primary 22; 17; 33
This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24–27, 2009, at Yale University.
Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work.
In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.
ReadershipGraduate students and research mathematicians interested in representation theory and connections between representation theory and mathematical physics.
-
Table of Contents
-
Expository papers
-
Rebecca A. Herb and Paul J. Sally, Jr. — The Plancherel formula, the Plancherel theorem, and the Fourier transform of orbital integrals
-
Toshiyuki Kobayashi — Branching problems of Zuckerman derived functor modules
-
Bong H. Lian, Andrew R. Linshaw and Bailin Song — Chiral equivariant cohomology of spheres
-
Research papers
-
Jeffrey Adams — Computing global characters
-
Dan M. Barbasch and Peter E. Trapa — Stable combinations of special unipotent representations
-
Elizabeth Dan-Cohen and Ivan Penkov — Levi components of parabolic subalgebras of finitary Lie algebras
-
Howard Garland — On extending the Langlands-Shahidi method to arithmetic quotients of loop groups
-
Michael W. Hero, Jeb F. Willenbring and Lauren Kelly Williams — The measurement of quantum entanglement and enumeration of graph coverings
-
Dan Lu and Roger Howe — The dual pair $(O_{p,q}, O\widetilde {Sp}_{2,2})$ and Zuckerman translation
-
Bertram Kostant and Nolan Wallach — On the algebraic set of singular elements in a complex simple Lie algebra
-
A. Garrett Lisi — An explicit embedding of gravity and the standard model in $E_8$
-
G. Lusztig — From groups to symmetric spaces
-
G. Lusztig — Study of antiorbital complexes
-
Stephen D. Miller and Wilfried Schmid — Adelization of automorphic distributions and mirabolic Eisenstein series
-
Ivan Penkov and Vera Serganova — Categories of integrable $sl(\infty )-, o(\infty )-, sp(\infty )$-modules
-
Siddhartha Sahi — Binomial coefficients and Littlewood-Richardson coefficients for interpolation polynomials and Macdonald polynomials
-
Birgit Speh — Restriction of some representations of $U(p,q)$ to a symmetric subgroup
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
This volume contains the proceedings of the conference on Representation Theory and Mathematical Physics, in honor of Gregg Zuckerman's 60th birthday, held October 24–27, 2009, at Yale University.
Lie groups and their representations play a fundamental role in mathematics, in particular because of connections to geometry, topology, number theory, physics, combinatorics, and many other areas. Representation theory is one of the cornerstones of the Langlands program in number theory, dating to the 1970s. Zuckerman's work on derived functors, the translation principle, and coherent continuation lie at the heart of the modern theory of representations of Lie groups. One of the major unsolved problems in representation theory is that of the unitary dual. The fact that there is, in principle, a finite algorithm for computing the unitary dual relies heavily on Zuckerman's work.
In recent years there has been a fruitful interplay between mathematics and physics, in geometric representation theory, string theory, and other areas. New developments on chiral algebras, representation theory of affine Kac-Moody algebras, and the geometric Langlands correspondence are some of the focal points of this volume. Recent developments in the geometric Langlands program point to exciting connections between certain automorphic representations and dual fibrations in geometric mirror symmetry.
Graduate students and research mathematicians interested in representation theory and connections between representation theory and mathematical physics.
-
Expository papers
-
Rebecca A. Herb and Paul J. Sally, Jr. — The Plancherel formula, the Plancherel theorem, and the Fourier transform of orbital integrals
-
Toshiyuki Kobayashi — Branching problems of Zuckerman derived functor modules
-
Bong H. Lian, Andrew R. Linshaw and Bailin Song — Chiral equivariant cohomology of spheres
-
Research papers
-
Jeffrey Adams — Computing global characters
-
Dan M. Barbasch and Peter E. Trapa — Stable combinations of special unipotent representations
-
Elizabeth Dan-Cohen and Ivan Penkov — Levi components of parabolic subalgebras of finitary Lie algebras
-
Howard Garland — On extending the Langlands-Shahidi method to arithmetic quotients of loop groups
-
Michael W. Hero, Jeb F. Willenbring and Lauren Kelly Williams — The measurement of quantum entanglement and enumeration of graph coverings
-
Dan Lu and Roger Howe — The dual pair $(O_{p,q}, O\widetilde {Sp}_{2,2})$ and Zuckerman translation
-
Bertram Kostant and Nolan Wallach — On the algebraic set of singular elements in a complex simple Lie algebra
-
A. Garrett Lisi — An explicit embedding of gravity and the standard model in $E_8$
-
G. Lusztig — From groups to symmetric spaces
-
G. Lusztig — Study of antiorbital complexes
-
Stephen D. Miller and Wilfried Schmid — Adelization of automorphic distributions and mirabolic Eisenstein series
-
Ivan Penkov and Vera Serganova — Categories of integrable $sl(\infty )-, o(\infty )-, sp(\infty )$-modules
-
Siddhartha Sahi — Binomial coefficients and Littlewood-Richardson coefficients for interpolation polynomials and Macdonald polynomials
-
Birgit Speh — Restriction of some representations of $U(p,q)$ to a symmetric subgroup
