Selberg integrals, Askey-Wilson polynomials and lozenge

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All these results have interesting applications in both mathematics and physics, particularly Abstract. The present paper is a report on joint work with Alessandro Languasco and Alberto Perelli, collected in [10], [11] and [12], on our recent investigations on the Selberg integral and its connections to Montgomery's pair-correlation function. integrals on split orthogonal groups. Recently, Hundley-Shen [9] gave a two-variable integral on GSp 4 GL 2 GL representing the product of two GL -twisted spin L-functions, one coming from each GL 2-factor. We found in [12] a two-variable Rankin-Selberg integral on GSp 4 GL 2. Such integrals are valuable for many reasons. 2019-11-01 · The grassmannian and the Selberg integral.

Selberg integral

References. Albion S.P., Rains E.M., The applications are given to the meromorphic extension of the Selberg integral as a function of its dimension and the scaling invariance of the underlying The Rankin-Selberg integral representation of Kohnen-Skoruppa [8] produces the Spin L-function for holomorphic Siegel modular cusp forms on GSp4. In mathematics the Selberg integral is a generalization of Euler beta function to n dimensions introduced by Atle Selberg (1944). Selberg-Askey integral. 6. Baker & Forrester Integral. 7.

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2019-11-01 q-SELBERG INTEGRALS AND MACDONALD POLYNOMIALS S. OLE WARNAAR Dedicated to Richard Askey on the occasion of his 70th birthday Abstract. Using the theory of Macdonald polynomials, a number of q-integrals of Selberg type are proved.

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(¾;ˆ) pairs 21 5. A generalization of Selberg’s beta integral involving Schur polynomials associated with partitions with entries not greater than 2 is explicitly computed.

M n ( a, b, γ) = ∏ j = 0 n − 1 Γ ( 1 + a + b + j γ) Γ ( 1 + ( j + 1) γ) Γ ( 1 + a + j γ) Γ ( 1 + b + j γ) Γ ( 1 + γ), for a, b, γ ∈ C such that ℜ ( a + b + 1) > 0, ℜ ( γ) > − min { 1 n, ℜ ( a + b + 1) n − 1 } . 2020-11-29 Multivariate Rankin–Selberg Integrals on GL4 and GU(2, 2) - Volume 61 Issue 4 Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites.
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The formula is 2019-09-01 2009-12-09 The Selberg integral is the following integral first evaluated by Selberg [6] in 1944 : (1.1)). Prasad, Multivariable I. where n is a positive integer, a, b and c are the complex number such that. We refer the reader to Forrester and Warnaar’s exposition [2] for the history and importance of the Selberg integral. 2019-11-01 q-SELBERG INTEGRALS AND MACDONALD POLYNOMIALS S. OLE WARNAAR Dedicated to Richard Askey on the occasion of his 70th birthday Abstract. Using the theory of Macdonald polynomials, a number of q-integrals of Selberg type are proved.

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My question is about the derivation from Selberg integral to Dyson integral in this paper: Selberg integral : $$ S_n(\alpha,\beta,\gamma) := \int_0 ^1 \cdots \int_0 ^1 \prod_{j=1}^n t_j^{\alpha- A new q-binomial theorem for Macdonald polynomials is employed to prove an A n analogue of the celebrated Selberg integral.