Elliptic hypergeometric series on root systems

By Hjalmar Rosengren. 2002

90 citations recorded by the source corpus.

Abstract We derive a number of summation and transformation formulas for elliptic hypergeometric series on the root systems A n , C n and D n . In the special cases of classical and q -series, our approach leads to new elementary proofs of the corresponding identities.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/62d05cc8fdedf5a9e1a89fb22a5504f4302f0c58

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Mathematical Physics

Citations in the corpus

Elliptic determinant evaluations and the Macdonald identities for affine root systems (2005, methodology): “Warnaar used it to obtain a summation formula for a multidimensional elliptic hypergeometric series; further related applications may be found in [R1], [ R2 ], [RS1], [Sp].”
Multiple Hypergeometric Series: Appell Series and Beyond (2013, background): “In particular, here we do not treat multiple hypergeometric series associated with root systems [16, 20, 25, 29], hypergeometric series of matrix argument [15], and other types of multivariate hypergeometric series such as those which mainly appear in the study of orthogonal polynomials of severable”
Transformations of elliptic hypergeometric integrals (2010, methodology): “Remark. A similar inductive argument based on a determinantal case was applied in [ 25 ] to prove the summation”
Extensions of the well-poised and elliptic well-poised Bailey lemma (2003, background): “ 10V9(a;b,c,d,e,q−n;q,p) = (aq,aq/bc,aq/bd,aq/cd;q,p) n (aq/b,aq/c,aq/d,aq/bcd;q,p) n , where bcde = a2qn+1. For a more extensive introduction to elliptic hypergeometric series we refer the reader to [6,7,8,9,10,12,14,15,16,18,19,20,21,23]. As our ﬁrst application of elliptic hypergeometric series w”
Multilateral Inversion of Ar, Cr, and Dr Basic Hypergeometric Series (2006, background): “Milne, and their co-workers, and later others (see [11, 12, 17, 18, 20, 21] for a very small selection of papers in this area).”
Multiple elliptic hypergeometric series. An approach from the Cauchy determinant (2003, methodology): “Multiple elliptic hypergeometric series are also generalized by means of root systems [ 15 ].”
Advanced Determinant Calculus: A Complement (2005, background): “For example, determinant evaluations involving elliptic functions have come into the picture in the theory of multiple elliptic hypergeometric series, see [88, 134, 138, 139, 141, 163, 174].”
$BC_n$-symmetric abelian functions (2004, methodology): “(This includes the BCn-type sum of [19], since as observed there, that sum can be obtained by specializing Warnaar’s Schlosser-type identity.”
Transformations of elliptic hypergometric integrals (2003, methodology): “A similar inductive argument based on a determinantal case was applied in [25] to prove the summation analogue of Corollary 3.”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “These expansions into “simple” fractions for theta functions were used in the papers [33, 36, 86] for the proof of some exact summation and integration formulae for elliptic hypergeometric functions.”