A q-analog of transposition symmetry for invariant G-functions
type: Item
instance of: scholarly article
title: A q-analog of transposition symmetry for invariant G-functions
zbMATH Open document ID: 0587.33010
DOI: 10.1016/0022-247X(86)90079-X
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: We give an algebraic construction of Milne's \(^{\nu}_{\mu}[G]_ m^{(n)}\) (\(\gamma\) ;\(\delta\) ;z) functions in terms of the matrix coefficients of certain linear operators \(B_{\mu z}\). We show that the \(^{\nu}_{\mu}[G]_ m^{(n)}\) (\(\gamma\) ;\(\delta\) ;z) functions all satisfy ''transposition'' symmetry if and only if \(z=(t,...,t)\in {\mathbb{C}}^ n\), unless \(^{\nu}_{\mu}[G]_ 1^{(n)}\) (\(\gamma\) ;\(\xi\) ;z) is identically zero. This transposition symmetry is a ''q-analog'' of that for the ordinary \(^{\nu}_{\mu}G_ m^{(n)}\) (\(\gamma\) ;\(\delta)\) polynomials of Biedenharn, Gustafson, and Milne. We also define a ''q-analog'' of the elementary reduced Wigner coefficients for U(n) and give both a combinatorial and representation theoretic interpretation of this definition.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 81R10
zbMATH DE Number: 3941957
zbMATH Keywords: G-functions
zbMATH Keywords: polynomials of Biedenharn
zbMATH Keywords: Wigner coefficients
author: Robert A. Gustafson
author: Stephen C. Milne
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3941957