Jordan Algebras and Quantum Bessel Processes

被引：0

作者：

Matysiak, Wojciech ^{[1
]}

Swieca, Marcin ^{[1
]}

机构：

[1] Warsaw Univ Sci & Technol, Wydzial Matemat & Nauk Informacyjnych, Ul Koszykowa 75, PL-00662 Warsaw, Poland

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2017年 / 2017卷 / 13期

关键词：

HEISENBERG; POLYNOMIALS;

D O I：

10.1093/imrn/rnw138

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A family of multidimensional Markov processes is constructed by restricting a semigroup of positive contractions on C*(H), where H = W x R is a Heisenberg group and W is a simple complex Jordan algebra, to some commutative sub-C*-algebras of C*(H), associated with certain Gelfand pairs. The constructed processes are multidimensional generalizations of Biane's quantum Bessel process. As a bonus, a construction of the quantum Bessel process related to the space of rectangular complex matrices is presented.

引用

页码：4029 / 4068

页数：40

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[1] BESSEL-FUNCTIONS ON JORDAN ALGEBRAS
DIB, H
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1990, 69 (04): : 403 - 448
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[J]. LECTURE NOTES IN MATHEMATICS, 1988, 1359 : 122 - 134
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[5] QUANTUM MEASURES AND STATES ON JORDAN ALGEBRAS
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[6] BESSEL-FUNCTIONS ASSOCIATED WITH REPRESENTATIONS OF FORMALLY REAL JORDAN ALGEBRAS
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[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 71 (01) : 123 - 141
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