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13
ELLIPTIC HYPERGEOMETRIC SERIES ON ROOT SYSTEMS
, 2002
"... We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems An, Cn and Dn. In the special cases of classical and qseries, our approach leads to new elementary proofs of the corresponding identities. ..."
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Cited by 36 (10 self)
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We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems An, Cn and Dn. In the special cases of classical and qseries, our approach leads to new elementary proofs of the corresponding identities.
Multiple Elliptic Hypergeometric Series. An Approach from the Cauchy Determinant
 Indag. Math
"... In this paper we investigate a multiple generalization of elliptic hypergeometric series, and propose a duality transformation for multiple hypergeometric series. Our duality transformation is obtained from an identity arising from the Cauchy determinant formula for the Weierstrass sigma function, b ..."
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Cited by 27 (2 self)
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In this paper we investigate a multiple generalization of elliptic hypergeometric series, and propose a duality transformation for multiple hypergeometric series. Our duality transformation is obtained from an identity arising from the Cauchy determinant formula for the Weierstrass sigma function, by means of specialization
Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations
 INDAG. MATH
, 2003
"... Using multiple qintegrals and a determinant evaluation, we establish a multivariable extension of Bailey’s nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive ..."
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Cited by 14 (6 self)
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Using multiple qintegrals and a determinant evaluation, we establish a multivariable extension of Bailey’s nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive new multivariable 1ψ1 summations. Some of our results are extended to the case of elliptic hypergeometric series.
BISYMMETRIC FUNCTIONS, MACDONALD POLYNOMIALS AND sl3 BASIC HYPERGEOMETRIC SERIES
, 2005
"... Abstract. A new class of sl3 basic hypergeometric series with Macdonald polynomial argument is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a keyingredient in the sl3 basic hypergeometric series is a bisymmetric function related to the sl3 Selberg ..."
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Cited by 11 (4 self)
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Abstract. A new class of sl3 basic hypergeometric series with Macdonald polynomial argument is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a keyingredient in the sl3 basic hypergeometric series is a bisymmetric function related to the sl3 Selberg integrals of Tarasov and Varchenko, and to alternating sign matrices. 1.
THE BAILEY LEMMA AND KOSTKA POLYNOMIALS
, 2002
"... Using the theory of Kostka polynomials, we prove an An−1 version of Bailey’s lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A (1) n−1 and to identities for A ..."
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Cited by 7 (1 self)
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Using the theory of Kostka polynomials, we prove an An−1 version of Bailey’s lemma at integral level. Exploiting a new, conjectural expansion for Kostka numbers, this is then generalized to fractional levels, leading to a new expression for admissible characters of A (1) n−1 and to identities for Atype branching functions.
Macdonald Polynomials and Multivariable Basic Hypergeometric Series
 SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS
, 2007
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Nonsymmetric interpolation Macdonald polynomials and gln basic hypergeometric series
, 2008
"... The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the wellknown Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gl n. Our main results include a new ..."
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Cited by 3 (2 self)
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The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the wellknown Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gl n. Our main results include a new qbinomial theorem, new qGauss sum, and several
A NEW MULTIVARIABLE 6ψ 6 SUMMATION FORMULA
, 2006
"... Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson’s 8φ7 summation formula by Milne, a new multivariable 8φ7 summation is derived. By a polynomial argument this 8φ7 summation is transformed to another multivariable 8φ7 summation which, by taking a suitable limit ..."
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Cited by 2 (0 self)
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Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson’s 8φ7 summation formula by Milne, a new multivariable 8φ7 summation is derived. By a polynomial argument this 8φ7 summation is transformed to another multivariable 8φ7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6φ5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey’s verywellpoised 6ψ6 summation formula.
A NONTERMINATING 8φ7 SUMMATION FOR THE ROOT System Cr
, 2002
"... Using multiple qintegrals and a determinant evaluation, we establish a nonterminating 8φ7 summation for the root system Cr. We also give some important specializations explicitly. ..."
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Using multiple qintegrals and a determinant evaluation, we establish a nonterminating 8φ7 summation for the root system Cr. We also give some important specializations explicitly.
Symmetry Groups of An Hypergeometric Series ⋆
"... Abstract. Structures of symmetries of transformations for Holman–Biedenharn–Louck An hypergeometric series: An terminating balanced 4F3 series and An elliptic 10E9 series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each ty ..."
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Abstract. Structures of symmetries of transformations for Holman–Biedenharn–Louck An hypergeometric series: An terminating balanced 4F3 series and An elliptic 10E9 series are discussed. Namely the description of the invariance groups and the classification all of possible transformations for each types of An hypergeometric series are given. Among them, a “periodic ” affine Coxeter group which seems to be new in the literature arises as an invariance group for a class of An 4F3 series. Key words: groups multivariate hypergeometric series; elliptic hypergeometric series; Coxeter