On polynomial integrals over the orthogonal group

被引：9

作者：

Banica, Teodor ^{[1
]}

Collins, Benoit ^{[2
,3
]}

Schlenker, Jean-Marc ^{[4
]}

机构：

[1] Cergy Pontoise Univ, Dept Math, F-95000 Cergy Pontoise, France

[2] Univ Lyon 1, Dept Math, F-69622 Villeurbanne, France

[3] Univ Ottawa, Ottawa, ON K1N 6N5, Canada

[4] Univ Toulouse 3, CNRS, Inst Math Toulouse, UMR 5219, F-31062 Toulouse 9, France

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2011年 / 118卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Orthogonal group; Haar measure; Hyperspherical law; UNITARY;

D O I：

10.1016/j.jcta.2010.11.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider integrals of type integral(on)u(11)(a1) ... u(1n)(an)u(21)(b1) ... u(2n)(bn)du, with respect to the Haar measure on the orthogonal group. We establish several remarkable invariance properties satisfied by such integrals, by using combinatorial methods. We present as well a general formula for such integrals, as a sum of products of factorials. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：778 / 795

页数：18

共 15 条

[1]

[Anonymous], 1990, Adv. Stud. Contemp. Math.

[2] On Orthogonal Matrices Maximizing the 1-norm [J].

Banica, Teodor ;

Collins, Benoit ;

Schlenker, Jean-Marc .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2010, 59 (03) :839-856

[3] Quantum Isometries and Noncommutative Spheres [J].

Banica, Teodor ;

Goswami, Debashish .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 298 (02) :343-356

[4] The Orthogonal Weingarten Formula in Compact Form [J].

Banica, Teodor .

LETTERS IN MATHEMATICAL PHYSICS, 2010, 91 (02) :105-118

[5] Spectral Analysis of the Free Orthogonal Matrix [J].

Banica, Teodor ;

Collins, Benoit ;

Zinn-Justin, Paul .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2009, 2009 (17) :3286-3309

[6] Integration with respect to the Haar measure on unitary, orthogonal and symplectic group [J].

Collins, B ;

Sniady, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 264 (03) :773-795

[7]

Curran S, 2010, T AM MATH SOC, V362, P4831

[8] ON THE EIGENVALUES OF RANDOM MATRICES [J].

DIACONIS, P ;

SHAHSHAHANI, M .

JOURNAL OF APPLIED PROBABILITY, 1994, 31A :49-62

[9]

MATSUMOTO S, DISCRETE MA IN PRESS

[10] Hua-type integrals over unitary groups and over projective limits of unitary groups [J].

Neretin, YA .

DUKE MATHEMATICAL JOURNAL, 2002, 114 (02) :239-266

← 1 2 →