**Contemporary Mathematics**

Volume: 490;
2009;
251 pp;
Softcover

MSC: Primary 16; 17; 20; 32; 51; 60; 81;

Print ISBN: 978-0-8218-4731-2

Product Code: CONM/490

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

**Electronic ISBN: 978-0-8218-8169-9
Product Code: CONM/490.E**

List Price: $83.00

AMS Member Price: $66.40

MAA Member Price: $74.70

# Symmetry in Mathematics and Physics

Share this page *Edited by *
*Donald Babbitt; Vyjayanthi Chari; Rita Fioresi*

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.

#### Readership

Graduate students and research mathematicians interested in mathematical physics.

# Table of Contents

## Symmetry in Mathematics and Physics

- Contents v7 free
- Preface vii9 free
- Probability 111 free
- The Role of Weak Convergence in Probability Theory 313
- Foundations of Quantum Mechanics 1121
- Statistical models on a simplex 1323
- Quantum Error Correcting Codes 2737
- Quantum Error Correcting Codes and Weyl Commutation Relations 2939
- Finite and Infinite Dimensional Lie Groups and Algebras and their Representations 4555
- Ideals in parabolic subalgebras of simple Lie algebras 4757
- Quantizations of modules of differential operators 6171
- Geometric realization of PRV components and the Littlewood-Richardson cone 8393
- Kaç algebras, quantum doubles and planar algebras 97107
- On a theorem of Ranee Brylinski 105115
- Conjugacy of maximal toral subalgebras of direct limits of loop algebras 133143
- A multiplicity formula for tensor products of SL2 modules and an explicit Sp2n to Sp2n−2 × Sp2 branching formula 151161
- Super Lie Groups and Supergeometry 157167
- Super G-spaces 159169
- Quotients in Supergeometry 177187
- Special geometry of D = 4, 5 supersymmetry 189199
- Supersymmetry 201211
- Symmetric Spaces in Supergravity 203213
- Symmetry and Superstring Phenomenology 229239
- Supersymmetry: A personal view 241251