eBook ISBN:  9780821882368 
Product Code:  CONM/557.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821882368 
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 KacMoody 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 DanCohen and Ivan Penkov — Levi components of parabolic subalgebras of finitary Lie algebras

Howard Garland — On extending the LanglandsShahidi 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 LittlewoodRichardson coefficients for interpolation polynomials and Macdonald polynomials

Birgit Speh — Restriction of some representations of $U(p,q)$ to a symmetric subgroup


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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 KacMoody 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 DanCohen and Ivan Penkov — Levi components of parabolic subalgebras of finitary Lie algebras

Howard Garland — On extending the LanglandsShahidi 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 LittlewoodRichardson coefficients for interpolation polynomials and Macdonald polynomials

Birgit Speh — Restriction of some representations of $U(p,q)$ to a symmetric subgroup