**American Mathematical Society Translations - Series 2
Advances in the Mathematical Sciences**

1996; 236 pp; Hardcover

MSC: Primary 22; 47; 81;

Print ISBN: 978-0-8218-0426-1

Product Code: TRANS2/175

Print ISBN: 978-0-8218-0426-1

Product Code: TRANS2/175

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

**Electronic ISBN: 978-1-4704-3386-4
Product Code: TRANS2/175.E**

List Price: $126.00

AMS Member Price: $100.80

MAA Member Price: $113.40

# Contemporary Mathematical Physics

Share this page *Edited by *
*R. L. Dobrushin; R. A. Minlos; M. A. Shubin; A. M. Vershik*

This first of a two-volume collection is a celebration of
the scientific heritage of F. A. Berezin (1931–1980). Before
his untimely death, Berezin had an important influence on physics
and mathematics, discovering new ideas in mathematical
physics, representation theory, analysis, geometry, and other areas
of mathematics. His crowning achievements were the introduction of a
new notion of deformation quantization, and Grassmannian
analysis (“supermathematics”).

Collected here are papers by his many of his colleagues and
others who worked in related areas, representing a wide spectrum of
topics in mathematical physics and allied areas of mathematics. In
particular, the papers discuss quantization, invariant integration,
spectral theory, and representation theory.

#### Readership

Graduate students and research mathematicians interested in group representation theory, supermathematics, and spectral analysis.

# Table of Contents

## Contemporary Mathematical Physics

- Cover Cover11
- Frontispiece iv5
- Title page v6
- Copyright page vi7
- Contents vii8
- Foreword ix10
- Felix Alexandrovich Berezin (A brief scientific biography) 112
- On the functional equation related to the quantum three-body problem 1526
- The differential calculus on quantum linear groups 3546
- The Penrose transform on flag domains in ℱ(ℂℙ²) 4960
- Defining relations associated with principal 𝔰𝔩(2)-subalgebras 5768
- A generalization of the Berezin-Lieb inequality 6980
- Quantization on para-Hermitian symmetric spaces 8192
- Integral operators with Gaussian kernels and symmetries of canonical commutation relations 97108
- Ergodic unitarily invariant measures on the space of infinite Hermitian matrices 137148
- Cogitations over Berezin’s integral 177188
- Remarks on the topology of the Hilbert Grassmannian 191202
- Asymptotic completeness 199210
- Constructive modules and the reductivity problem in the category 𝒪 207218
- Alik Berezin in the recollections of friends 225236
- Back Cover Back Cover1249