A generalization of mehta-wang determinant and askey-wilson polynomials

Victor J.W. Guo, Masao Ishikawa, Hiroyuki Tagawa, Jiang Zeng

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)

Abstract

Motivated by the Gaussian symplectic ensemble, Mehta andWang 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 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.

Original languageEnglish
Pages (from-to)719-730
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
Publication statusPublished - Nov 18 2013
Externally publishedYes
Event25th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2013 - Paris, France
Duration: Jun 24 2013Jun 28 2013

Keywords

  • The askey-wilson polynomials
  • The mehta-wang determinants
  • The moments of the little q-jacobi polynomials

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)
  • Discrete Mathematics and Combinatorics

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