Contents

Preface vii

Probability

The Role of Weak Convergence in Probability Theory

S. R. S. Varadhan 3

Foundations of Quantum Mechanics

Statistical models on a simplex

Enrico G. Beltrametti 13

Quantum Error Correcting Codes

Quantum Error Correcting Codes and Weyl Commutation Relations

K. R. Parthasarathy 29

Finite and Inﬁnite Dimensional Lie Groups and Algebras

and their Representations

Ideals in parabolic subalgebras of simple Lie algebras

Vyjayanthi Chari, R. J. Dolbin, and T. Ridenour 47

Quantizations of modules of diﬀerential operators

Charles H. Conley 61

Geometric realization of PRV components and the Littlewood-Richardson cone

Ivan Dimitrov and Mike Roth 83

Ka¸ c algebras, quantum doubles and planar algebras

S. Jijo and V. S. Sunder 97

On a theorem of Ranee Brylinski

Bertram Kostant and Nolan Wallach 105

Conjugacy of maximal toral subalgebras of direct limits of loop algebras

Hadi Salmasian 133

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