Victor J. W. Guo ; Masao Ishikawa ; Hiroyuki Tagawa ; Jiang Zeng - A generalization of Mehta-Wang determinant and Askey-Wilson polynomials

dmtcs:2337 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2337
A generalization of Mehta-Wang determinant and Askey-Wilson polynomialsArticle

Authors: Victor J. W. Guo ORCID1; Masao Ishikawa 2; Hiroyuki Tagawa 3; Jiang Zeng ORCID4

  • 1 Department of Mathematics, East China Normal University
  • 2 Department of Mathematics [Okinawa]
  • 3 Department of Mathematics [Wakayama]
  • 4 Institut Camille Jordan

Motivated by the Gaussian symplectic ensemble, Mehta and Wang evaluated the $n×n$ determinant $\det ((a+j-i)Γ (b+j+i))$ in 2000. When $a=0$, Ciucu and Krattenthaler computed the associated Pfaffian $\mathrm{Pf}((j-i)Γ (b+j+i))$ with an application to the two dimensional dimer system in 2011. Recently we have generalized the latter Pfaffian formula with a $q$-analogue by replacing the Gamma function by the moment sequence of the little $q$-Jacobi polynomials. On the other hand, Nishizawa has found a q-analogue of the Mehta–Wang formula. Our purpose is to generalize both the Mehta-Wang and Nishizawa formulae by using the moment sequence of the little $q$-Jacobi polynomials. It turns out that the corresponding determinant can be evaluated explicitly in terms of the Askey-Wilson polynomials.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: The Mehta-Wang determinants,the moments of the little q-Jacobi polynomials,the Askey-Wilson polynomials.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

Consultation statistics

This page has been seen 227 times.
This article's PDF has been downloaded 305 times.