eBook ISBN:  9780821877364 
Product Code:  CONM/145.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821877364 
Product Code:  CONM/145.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 145; 1993; 491 ppMSC: Primary 22; 46
Touching on virtually every important topic in modern representation theory, this book contains proceedings of the activities of the Representation Theory Group at the University of Maryland at College Park during the years 1989–1992. Covered here are the latest results in the field, providing a readable introduction to the work of some of the best young researchers in representation theory. The book spans a very broad spectrum—for example, within real representation theory, both semisimple and nonsemisimple analysis are discussed; within \(C^*\)algebras, both geometric and nongeometric approaches are studied. In addition, the articles are exceptionally well written and range from research papers aimed at specialists to expository articles accessible to graduate students.
ReadershipGraduate students and research mathematicians in representation theory.

Table of Contents

Part I. Keynote speakers [ MR 1216178 ]

Aleksandr Aleksandrovich Kirillov — The orbit method. I. Geometric quantization [ MR 1216179 ]

Aleksandr Aleksandrovich Kirillov — The orbit method. II. Infinitedimensional Lie groups and Lie algebras [ MR 1216180 ]

Joachim Cuntz — Quantized differential forms in noncommutative topology and geometry [ MR 1216181 ]

Gennadi Kasparov — Novikov’s conjecture on higher signatures: the operator $K$theory approach [ MR 1216182 ]

Dan Voiculescu — ${\rm II}_1$factors of free groups and random matrices [ MR 1216183 ]

Part II. $p$adic groups [ MR 1216178 ]

Thomas C. Hales — A simple definition of transfer factors for unramified groups [ MR 1216184 ]

Michael J. Heumos — Models and periods for automorphic forms on ${\rm GL}_n$ [ MR 1216185 ]

Lawrence Morris — The admissible dual via restriction to open compact subgroups [ MR 1216186 ]

Fiona Murnaghan — Asymptotic behaviour of supercuspidal characters [ MR 1216187 ]

Part III. Symmetric spaces, real groups, and the orbit method [ MR 1216178 ]

Erik van den Ban and Henrik Schlichtkrull — Multiplicities in the Plancherel decomposition for a semisimple symmetric space [ MR 1216188 ]

Chal Benson, Joe Jenkins and Gail Ratcliff — ${\rm O}(n)$spherical functions on Heisenberg groups [ MR 1216189 ]

Frédéric Bien — Orbits, multiplicities and differential operators [ MR 1216190 ]

Mogens FlenstedJensen — A simple approach to $D_\lambda $modules [ MR 1216191 ]

JianShu Li — Theta series and construction of automorphic forms [ MR 1216192 ]

Bong H. Lian and Gregg J. Zuckerman — An application of infinitedimensional Lie theory to semisimple Lie groups [ MR 1216193 ]

Hisayosi Matumoto — On the existence of homomorphisms between scalar generalized Verma modules [ MR 1216194 ]

Siddhartha Sahi — Unitary representations on the Shilov boundary of a symmetric tube domain [ MR 1216195 ]

W. Schmid and K. Vilonen — Characters, fixed points and Osborne’s conjecture [ MR 1216196 ]

David A. Vogan, Jr. — The local Langlands conjecture [ MR 1216197 ]

Part IV. $C^*$algebras [ MR 1216178 ]

Robert P. Boyer — Representation theory of infinitedimensional unitary groups [ MR 1216198 ]

Marius Dădărlat — $C^*$algebras and applications [ MR 1216199 ]

George A. Elliott — Are amenable $C^*$algebras classifiable

Elliot C. Gootman — Spectra for group actions [ MR 1216201 ]

Victor Nistor — Higher McKeanSinger index formulae and noncommutative geometry [ MR 1216202 ]

Robert T. Powers and Geoffrey L. Price — Binary shifts on the hyperfinite ${\rm II}_1$ factor [ MR 1216203 ]

Marc A. Rieffel — Compact quantum groups associated with toral subgroups [ MR 1216204 ]


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Touching on virtually every important topic in modern representation theory, this book contains proceedings of the activities of the Representation Theory Group at the University of Maryland at College Park during the years 1989–1992. Covered here are the latest results in the field, providing a readable introduction to the work of some of the best young researchers in representation theory. The book spans a very broad spectrum—for example, within real representation theory, both semisimple and nonsemisimple analysis are discussed; within \(C^*\)algebras, both geometric and nongeometric approaches are studied. In addition, the articles are exceptionally well written and range from research papers aimed at specialists to expository articles accessible to graduate students.
Graduate students and research mathematicians in representation theory.

Part I. Keynote speakers [ MR 1216178 ]

Aleksandr Aleksandrovich Kirillov — The orbit method. I. Geometric quantization [ MR 1216179 ]

Aleksandr Aleksandrovich Kirillov — The orbit method. II. Infinitedimensional Lie groups and Lie algebras [ MR 1216180 ]

Joachim Cuntz — Quantized differential forms in noncommutative topology and geometry [ MR 1216181 ]

Gennadi Kasparov — Novikov’s conjecture on higher signatures: the operator $K$theory approach [ MR 1216182 ]

Dan Voiculescu — ${\rm II}_1$factors of free groups and random matrices [ MR 1216183 ]

Part II. $p$adic groups [ MR 1216178 ]

Thomas C. Hales — A simple definition of transfer factors for unramified groups [ MR 1216184 ]

Michael J. Heumos — Models and periods for automorphic forms on ${\rm GL}_n$ [ MR 1216185 ]

Lawrence Morris — The admissible dual via restriction to open compact subgroups [ MR 1216186 ]

Fiona Murnaghan — Asymptotic behaviour of supercuspidal characters [ MR 1216187 ]

Part III. Symmetric spaces, real groups, and the orbit method [ MR 1216178 ]

Erik van den Ban and Henrik Schlichtkrull — Multiplicities in the Plancherel decomposition for a semisimple symmetric space [ MR 1216188 ]

Chal Benson, Joe Jenkins and Gail Ratcliff — ${\rm O}(n)$spherical functions on Heisenberg groups [ MR 1216189 ]

Frédéric Bien — Orbits, multiplicities and differential operators [ MR 1216190 ]

Mogens FlenstedJensen — A simple approach to $D_\lambda $modules [ MR 1216191 ]

JianShu Li — Theta series and construction of automorphic forms [ MR 1216192 ]

Bong H. Lian and Gregg J. Zuckerman — An application of infinitedimensional Lie theory to semisimple Lie groups [ MR 1216193 ]

Hisayosi Matumoto — On the existence of homomorphisms between scalar generalized Verma modules [ MR 1216194 ]

Siddhartha Sahi — Unitary representations on the Shilov boundary of a symmetric tube domain [ MR 1216195 ]

W. Schmid and K. Vilonen — Characters, fixed points and Osborne’s conjecture [ MR 1216196 ]

David A. Vogan, Jr. — The local Langlands conjecture [ MR 1216197 ]

Part IV. $C^*$algebras [ MR 1216178 ]

Robert P. Boyer — Representation theory of infinitedimensional unitary groups [ MR 1216198 ]

Marius Dădărlat — $C^*$algebras and applications [ MR 1216199 ]

George A. Elliott — Are amenable $C^*$algebras classifiable

Elliot C. Gootman — Spectra for group actions [ MR 1216201 ]

Victor Nistor — Higher McKeanSinger index formulae and noncommutative geometry [ MR 1216202 ]

Robert T. Powers and Geoffrey L. Price — Binary shifts on the hyperfinite ${\rm II}_1$ factor [ MR 1216203 ]

Marc A. Rieffel — Compact quantum groups associated with toral subgroups [ MR 1216204 ]