✦ LIBER ✦

Schur functions, Good's identity, and hypergeometric series well poised in SU(n)

✍ Scribed by R.A Gustafson; S.C Milne

Book ID: 102978505
Publisher: Elsevier Science
Year: 1983
Tongue: English
Weight: 531 KB
Volume: 48
Category: Article
ISSN: 0001-8708
DOI: 10.1016/0001-8708(83)90088-9

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✦ Synopsis

A simple direct proof is given of a fundamental identity involving Schur functions which contains as special cases the identity responsible for Good's proof of the Dyson conjecture and the summation theorem of Biedenharn and Louck that appears frequently in dealing with the explicit matrix elements which arise in the unitary groups. By using the Weyl character formula, a general identity is obtained which implies our result involving Schur functions when a root system of type A, _ , is considered. As a further application of our general identity, explicit analogs of Good's identity are given, corresponding to the root systems of types B,, C,, and D,. In addition, methods to obtain q-analogs of all of these results are briefly described.

📜 SIMILAR VOLUMES

On Hypergeometric Series Well-Poised in

On Hypergeometric Series Well-Poised in $SU(n)$

✍ Holman, III, W. J.; Biedenharn, L. C.; Louck, J. D. 📂 Article 📅 1976 🏛 Society for Industrial and Applied Mathematics 🌐 English ⚖ 966 KB

A q-analog of the 5F4(1) summation theor

A q-analog of the 5F4(1) summation theorem for hypergeometric series well-poised in SU(n)

✍ S.C Milne 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 797 KB

As an application of a general q-difference equation for basic hypergeometric series well-poised in SU(n), an elementary proof is given of a q-analog of Holman's SU(n) generalization of the terminating sF4( 1) summation theorem. This provides an SC/(n) generalization of the terminating e@s summation