کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6419714 | 1631647 | 2011 | 33 صفحه PDF | دانلود رایگان |
A one-parameter rational function generalisation Rλ(X;b) of the symmetric Macdonald polynomial and interpolation Macdonald polynomial is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal specialisation formula and q-difference equation for Rλ(X;b). Our main motivation for studying Rλ(X;b) is that it leads to a new class of sln basic hypergeometric series, generalising the well-known basic hypergeometric series with Macdonald polynomial argument. For these new series we prove sln analogues of the q-Gauss and q-Kummer-Thomae-Whipple formulas. In a special limit, one of our results implies an elegant binomial formula for Jack polynomials, different to that of Kaneko, Lassalle, Okounkov and Olshanski.
Journal: Advances in Applied Mathematics - Volume 46, Issues 1â4, January 2011, Pages 424-456