Multilateral Summation Theorems for Ordinary and Basic Hypergeometric Series in $U(n)$.

Gustafson, Robert A.

doi:10.1137/0518114

Cited by 56 publications

(53 citation statements)

References 17 publications

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“…Multidimensional analogues of the Bailey 6 \j/ 6 and Dougall 5 F 4 summation formulas (1.2a), (1.2b) different from the ones in (2.22a)/(2.22b) were introduced by Gustafson in [Gul,Gu2] (cf. also Section 4), and recently still another multidimensional version (in two distinct variations) of the 6 \l/ 6 sum was presented by Schlosser [Sch].…”

Section: A Generalized Aomoto-ito Summentioning

confidence: 99%

On Certain Multiple Bailey, Rogers and Dougall Type Summation Formulas

Diejen¹

1997

Publ. Res. Inst. Math. Sci.

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A multidimensional generalization of Bailey's very-well-poised bilateral basic hypergeometric 6 \l/ 6 summation formula and its Dougall type 5 H 5 hypergeometric degeneration for q -> 1 is studied. The multiple Bailey sum amounts to an extension corresponding to the case of a nonreduced root system of certain summation identities associated to the reduced root systems that were recently conjectured by Aomoto and Ito and proved by Macdonald. By truncation, we obtain multidimensional analogues of the very-well poised unilateral (basic) hypergeometric Rogers 6 $ 5 and Dougall 5 jF 4 sums (both nonterminating and terminating). The terminating sums may be used to arrive at product formulas for the norms of recently introduced (#-)Racah polynomials in several variables.

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Section: A Generalized Aomoto-ito Summentioning

confidence: 99%

On Certain Multiple Bailey, Rogers and Dougall Type Summation Formulas

Diejen¹

1997

Publ. Res. Inst. Math. Sci.

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“…After finishing this work, Prof. C. Krattenthaller kindly gave us a comment that formula (1.12) is a special case of the 6 φ 6 Bailey summation theorem in SU(n) due to R. A. Gustafson [1]. Dr. M. Schlosser also pointed out that (1.13) is precisely Theorem 5.44 in S. C. Milne [7].…”

Section: Notes Addedmentioning

confidence: 99%

“…. ., we consider a q-difference operator B m which should satisfy the following condition: For any partition λ = (λ 1 [4,5]. We remark that, as to the Hall-Littlewood polynomials (the case when q = 0), such a class of raising operators B m of row type has been implicitly employed in Macdonald [6], Chapter III, (2.14)…”

Section: Introductionmentioning

confidence: 99%

“…. , α n ) ∈ N n , we set |α| = α 1 + · · · + α n and x α = x α 1 1 · · · x α n n , T α q,x = T α 1 q,x 1 · · · T α n q,x n , (1.4) where T q,x i is the q-shift operator in x i , defined by We will also determine the operator B m explicitly by an interpolation method. In the following, we use the notation α β for the partial ordering of multi-indices defined by…”

Section: Introductionmentioning

confidence: 99%

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Kajihara¹,

Noumi²

2000

Compositio Mathematica

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“…As result, many of the classical formulae for basic hypergeometric series from [12] have already been generalized to the setting of A n−1 series, see e.g. the references [5,10,13,14,35,36,38,39,40,42,43,49].…”

Section: Proposition 32 ((Milne) Anmentioning

confidence: 99%

Macdonald Polynomials and Multivariable Basic Hypergeometric Series

Schlosser¹

2007

SIGMA

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Abstract. We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6 φ 5 summation formula. We derive several new related identities including multivariate extensions of Jackson's verywell-poised 8 φ 7 summation. Motivated by our basic hypergeometric analysis, we propose an extension of Macdonald polynomials to Macdonald symmetric functions indexed by partitions with complex parts. These appear to possess nice properties.

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Multilateral Summation Theorems for Ordinary and Basic Hypergeometric Series in $U(n)$.

Cited by 56 publications

References 17 publications

On Certain Multiple Bailey, Rogers and Dougall Type Summation Formulas

On Certain Multiple Bailey, Rogers and Dougall Type Summation Formulas

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Macdonald Polynomials and Multivariable Basic Hypergeometric Series

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