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The importance of the Selberg integral (Q3528011)

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Language	Label	Description	Also known as
English	The importance of the Selberg integral	scientific article

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scholarly article

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The importance of the Selberg integral (English)

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zbMATH Open document ID

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10.1090/S0273-0979-08-01221-4

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Peter J. Forrester

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Bulletin of the American Mathematical Society

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publication date

2 October 2008

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full work available at URL

https://arxiv.org/abs/0710.3981

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Mathematics Subject Classification ID

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zbMATH DE Number

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MaRDI profile type

MaRDI publication profile

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A Short Proof of Selberg’s Generalized Beta Formula

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Another q-Extension of the Beta Function

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Jacobi Polynomials Associated with Selberg Integrals

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ON THE COMPLEX SELBERG INTEGRAL

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On a theta product formula for the symmetric \(A\)-type connection function

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On elliptic product formulas for Jackson integrals associated with reduced root systems

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Some Basic Hypergeometric Extensions of Integrals of Selberg and Andrews

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Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials

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Finite-\(N\) fluctuation formulas for random matrices

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The Calogero-Sutherland model and generalized classical polynomials

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Nonsymmetric Jack polynomials and integral kernels

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Generalized Jacobi polynomials and Selberg integrals

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Certain Hypergeometric Series Related to the Root System BC

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Proof of Serban’s conjecture

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A unification of Knizhnik-Zamolodchikov and Dunkl operators via affine Hecke algebras

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Double affine Hecke algebras and Macdonald's conjectures

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From double Hecke algebra to Fourier transform

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Asymptotics of multinomial sums and identities between multi-integrals

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Some Non-Central Distribution Problems in Multivariate Analysis

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On the Marginal Distributions of the Latent Roots of the Multivariate Beta Matrix

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Self-dual Koornwinder-Macdonald polynomials

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Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

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Matrix models for beta ensembles

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Differential-Difference Operators Associated to Reflection Groups

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Statistical Theory of the Energy Levels of Complex Systems. I

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Identities for products of Gauss sums over finite fields

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The evaluation of Selberg character sums

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Multidimensional <i>q</i>-Beta Integrals

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Selberg-Jack character sums of dimension 2

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Elliptic Selberg integrals and conformal blocks

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Recurrence equations for the computation of correlations in the \(1/r^2\) quantum many-body system

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A random matrix decimation procedure relating \(\beta = 2/( r + 1)\) to \(\beta = 2( r + 1)\)

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Interpretations of some parameter dependent generalizations of classical matrix ensembles

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A Proof of the Macdonald–Morris Root System Conjecture for $F_4 $

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Macdonald’s constant term conjectures for exceptional root systems

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Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels

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A generalization of Selberg’s beta integral

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Some <i>q</i>-Beta Integrals on $SU(n)$ and $Sp(n)$ That Generalize the Askey–Wilson and Nasrallah–Rahman Integrals

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Une <i>q</i>-Intégrale de Selberg et Askey

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An elementary approach to the hypergeometric shift operators of Opdam

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Bessel functions of matrix argument

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On a theta product formula for Jackson integrals associated with root systems of rank two

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Shape fluctuations and random matrices

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Non-intersecting paths, random tilings and random matrices

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A Proof of Askey’s Conjectured <i>q</i>-Analogue of Selberg’s Integral and a Conjecture of Morris

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A proof of the 𝑞-Macdonald-Morris conjecture for 𝐵𝐶_{𝑛}

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The Selberg-Jack symmetric functions

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Intertwining operators for a degenerate double affine Hecke algebra and multivariable orthogonal polynomials

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Selberg Integrals and Hypergeometric Functions Associated with Jack Polynomials

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$q$-Selberg integrals and Macdonald polynomials

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Geometry of moment spaces

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Zeroes of zeta functions and symmetry

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Random matrix theory and \(\zeta(1/2+it)\).

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Random matrix theory and \(L\)-functions at \(s=1/2\).

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Random matrices and<i>L</i>-functions

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Random matrix theory, the exceptional Lie groups and<i>L</i>-functions

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Current algebras and Wess-Zumino model in two dimensions

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Hankel hyperdeterminants and Selberg integrals

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Projection Formulas, a Reproducing Kernel and a Generating Function for <i>q</i>-Wilson Polynomials

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A <i>q</i>-Beta Integral Associated with $BC_1 $

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Properties of the Confluent Hypergeometric Function

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Statistical Theory of the Energy Levels of Complex Systems. V

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Reductibility and irreducibility of the Gauss-Manin system associated with a Selberg type integral

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The connection problem associated with a Selberg type integral and the <i>q</i>-Racah polynomials

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The reciprocity relation of the Selberg function.

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Intersection numbers of twisted cycles associated with the Selberg integral and an application to the conformal field theory

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A GENERALIZATION OF THE BETA INTEGRAL ARISING FROM THE KNIZHNIK-ZAMOLODCHIKOV EQUATION FOR THE VECTOR REPRESENTATIONS OF TYPES <i>B<sub>n</sub></i>, <i>C<sub>n</sub></i> AND <i>D<sub>n</sub></i>

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Systems of Partial Differential Equations for Hypergeometric Functions of Matrix Argument

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\(BC\)-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials

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Infinite wedge and random partitions

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Some applications of hypergeometric shift operators

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Lecture notes on Dunkl operators for real and complex reflection groups

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An integral Representation of a <sub>10</sub><i>ϕ</i><sub>9</sub> and Continuous Bi-Orthogonal <sub>10</sub><i>ϕ</i><sub>9</sub> Rational Functions

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Transformations of elliptic hypergeometric integrals

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Limits of elliptic hypergeometric integrals

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Determinants of elliptic hypergeometric integrals

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Asymptotic values for degrees associated with strips of Young diagrams

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Determinants of period matrices and an application to Selberg's multidimensional beta integral

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Computational methods and experiments in analytic number theory

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First order analytic difference equations and integrable quantum systems

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Arrangements of hyperplanes and Lie algebra homology

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On the elliptic beta function

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Short proofs of the elliptic beta integrals

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Rarefied elliptic hypergeometric functions

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Some combinatorial properties of Jack symmetric functions

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A Short Proof of MacDonald's Conjecture for the Root Systems of Type A

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Multivariable Big and Little q-Jacobi Polynomials

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On $BC$ type basic hypergeometric orthogonal polynomials

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Selberg-type integrals associated with \(\mathfrak{sl}_3\)

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\(q\)-Selberg integrals and Macdonald polynomials

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On the generalised Selberg integral of Richards and Zheng

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A Selberg integral for the Lie algebra \(A_n\)

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Proof of a Conjecture by Dyson

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A Class of Generalized Hypergeometric Functions in Several Variables

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A proof of Andrews' \(q\)-Dyson conjecture

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A Proof of the $G_2 $ Case of Macdonald’s Root System-Dyson Conjecture

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A Unified Approach to Macdonald’s Root-System Conjectures

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A Stembridge-Stanton style elementary proof of the Habsieger-Kadell q- Morris identity

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Mathematics(1 entry)

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