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Softcover ISBN:  9780821847312 
Product Code:  CONM/490 
List Price:  $130.00 
MAA Member Price:  $117.00 
AMS Member Price:  $104.00 
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Product Code:  CONM/490.E 
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MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821847312 
eBook ISBN:  9780821881699 
Product Code:  CONM/490.B 
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Book DetailsContemporary MathematicsVolume: 490; 2009; 251 ppMSC: Primary 16; 17; 20; 32; 51; 60; 81;
The articles in this volume mainly grew out of talks given at a Conference held at UCLA in January 2008, which honored V. S. Varadarajan on his 70th birthday. The main theme of the Conference was symmetry in mathematics and physics, areas of mathematics and mathematical physics in which Varadarajan has made significant contributions during the past 50 years. Very early in his career he also worked and made significant contributions in the areas of probability and the foundations of quantum mechanics.
Topics covered by the articles in this volume are probability, quantum mechanics, symmetry (broadly interpreted in mathematics and physics), finite and infinite dimensional Lie groups and Lie algebras and their representations, super Lie groups and supergeometry (relatively new but active and important fields at the interface between mathematics and physics), and supersymmetry. The latter topic takes on a special importance since one of the first experiments at the Large Hadron Collider at CERN will be a test of whether supersymmetry exists in the world of elementary particles. A reprint of an exposition of supersymmetry by one of its founders, B. Zumino, appears in this volume.
ReadershipGraduate students and research mathematicians interested in mathematical physics.

Table of Contents

Probability [ MR 2555965 ]

S. R. S. Varadhan — The role of weak convergence in probability theory [ MR 2555966 ]

Foundations of Quantum Mechanics [ MR 2555965 ]

Enrico G. Beltrametti — Statistical models on a simplex [ MR 2555967 ]

Quantum Error Correcting Codes [ MR 2555965 ]

K. R. Parthasarathy — Quantum error correcting codes and Weyl commutation relations [ MR 2555968 ]

Finite and Infinite Dimensional Lie Groups and Algebras and their Representations [ MR 2555965 ]

Vyjayanthi Chari, R. J. Dolbin and T. Ridenour — Ideals in parabolic subalgebras of simple Lie algebras [ MR 2555969 ]

Charles H. Conley — Quantizations of modules of differential operators [ MR 2555970 ]

Ivan Dimitrov and Mike Roth — Geometric realization of PRV components and the LittlewoodRichardson cone [ MR 2555971 ]

S. Jijo and V. S. Sunder — Kac algebras, quantum doubles and planar algebras [ MR 2555972 ]

Bertram Kostant and Nolan Wallach — On a theorem of Ranee Brylinski [ MR 2555973 ]

Hadi Salmasian — Conjugacy of maximal toral subalgebras of direct limits of loop algebras [ MR 2555974 ]

Nolan Wallach and Oded Yacobi — A multiplicity formula for tensor products of ${\rm SL}_2$ modules and an explicit ${\rm Sp}_{2n}$ to ${\rm Sp}_{2n2}\times {\rm Sp}_2$ branching formula [ MR 2555975 ]

Super Lie Groups and Supergeometry [ MR 2555965 ]

Luigi Balduzzi, Claudio Carmeli and Gianni Cassinelli — Super $G$spaces [ MR 2555976 ]

Luigi Balduzzi, Claudio Carmeli and Rita Fioresi — Quotients in supergeometry [ MR 2555977 ]

María Antonia Lledó and José Antonio López — Special geometry of $D=4,\ 5$ supersymmetry [ MR 2555978 ]

Supersymmetry [ MR 2555965 ]

Sergio Ferrara and Alessio Marrani — Symmetric spaces in supergravity [ MR 2555979 ]

Mary K. Gaillard — Symmetry and superstring phenomenology [ MR 2555980 ]

B. Zumino — Supersymmetry: a personal view [ MR 2555981 ]


Additional Material

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The articles in this volume mainly grew out of talks given at a Conference held at UCLA in January 2008, which honored V. S. Varadarajan on his 70th birthday. The main theme of the Conference was symmetry in mathematics and physics, areas of mathematics and mathematical physics in which Varadarajan has made significant contributions during the past 50 years. Very early in his career he also worked and made significant contributions in the areas of probability and the foundations of quantum mechanics.
Topics covered by the articles in this volume are probability, quantum mechanics, symmetry (broadly interpreted in mathematics and physics), finite and infinite dimensional Lie groups and Lie algebras and their representations, super Lie groups and supergeometry (relatively new but active and important fields at the interface between mathematics and physics), and supersymmetry. The latter topic takes on a special importance since one of the first experiments at the Large Hadron Collider at CERN will be a test of whether supersymmetry exists in the world of elementary particles. A reprint of an exposition of supersymmetry by one of its founders, B. Zumino, appears in this volume.
Graduate students and research mathematicians interested in mathematical physics.

Probability [ MR 2555965 ]

S. R. S. Varadhan — The role of weak convergence in probability theory [ MR 2555966 ]

Foundations of Quantum Mechanics [ MR 2555965 ]

Enrico G. Beltrametti — Statistical models on a simplex [ MR 2555967 ]

Quantum Error Correcting Codes [ MR 2555965 ]

K. R. Parthasarathy — Quantum error correcting codes and Weyl commutation relations [ MR 2555968 ]

Finite and Infinite Dimensional Lie Groups and Algebras and their Representations [ MR 2555965 ]

Vyjayanthi Chari, R. J. Dolbin and T. Ridenour — Ideals in parabolic subalgebras of simple Lie algebras [ MR 2555969 ]

Charles H. Conley — Quantizations of modules of differential operators [ MR 2555970 ]

Ivan Dimitrov and Mike Roth — Geometric realization of PRV components and the LittlewoodRichardson cone [ MR 2555971 ]

S. Jijo and V. S. Sunder — Kac algebras, quantum doubles and planar algebras [ MR 2555972 ]

Bertram Kostant and Nolan Wallach — On a theorem of Ranee Brylinski [ MR 2555973 ]

Hadi Salmasian — Conjugacy of maximal toral subalgebras of direct limits of loop algebras [ MR 2555974 ]

Nolan Wallach and Oded Yacobi — A multiplicity formula for tensor products of ${\rm SL}_2$ modules and an explicit ${\rm Sp}_{2n}$ to ${\rm Sp}_{2n2}\times {\rm Sp}_2$ branching formula [ MR 2555975 ]

Super Lie Groups and Supergeometry [ MR 2555965 ]

Luigi Balduzzi, Claudio Carmeli and Gianni Cassinelli — Super $G$spaces [ MR 2555976 ]

Luigi Balduzzi, Claudio Carmeli and Rita Fioresi — Quotients in supergeometry [ MR 2555977 ]

María Antonia Lledó and José Antonio López — Special geometry of $D=4,\ 5$ supersymmetry [ MR 2555978 ]

Supersymmetry [ MR 2555965 ]

Sergio Ferrara and Alessio Marrani — Symmetric spaces in supergravity [ MR 2555979 ]

Mary K. Gaillard — Symmetry and superstring phenomenology [ MR 2555980 ]

B. Zumino — Supersymmetry: a personal view [ MR 2555981 ]