排序方式: 共有27条查询结果,搜索用时 250 毫秒
1.
Alexander Berkovich S. Ole Warnaar 《Transactions of the American Mathematical Society》2005,357(6):2291-2351
Several new transformations for -binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found. The new -binomial transformations are also applied to obtain multisum Rogers-Ramanujan identities, to find new representations for the Rogers-Szegö polynomials, and to make some progress on Bressoud's generalized Borwein conjecture. For the original Borwein conjecture we formulate a refinement based on new triple sum representations of the Borwein polynomials.
2.
S. Ole Warnaar 《Journal of statistical physics》1996,84(1-2):49-83
We compute the one-dimensional configuration sums of the ABF model using the fermionic technique introduced in part I of this paper. Combined with the results of Andrews, Baxter, and Forrester, we prove polynomial identities for finitizations of the Virasoro characters
as conjectured by Melzer. In the thermodynamic limit these identities reproduce Rogers-Ramanujan-type identities for the unitary minimal Virasoro characters conjectured by the Stony Brook group. We also present a list of additional Virasoro character identities which follow from our proof of Melzer's identities and application of Bailey's lemma.Dedicated to the memory of Piet Kasteleyn. 相似文献
3.
4.
Three new summation formulas for 6
ψ
6 bilateral basic hypergeometric series attached to root systems are presented. Remarkably, two of these formulae, labelled
by the A2n−1 and A2n
root systems, can be reduced to multiple 6
φ
5 sums generalising the well-known van Diejen sum. This latter sum serves as the weight-function normalisation for the BC
n
q-Racah polynomials of van Diejen and Stokman. Two 8
φ
7-level extensions of the multiple 6
φ
5 sums, as well as their elliptic analogues, are conjectured. This opens up the prospect of constructing novel A-type extensions
of the Koornwinder–Macdonald theory. 相似文献
5.
S. Ole Warnaar 《Acta Mathematica》2009,203(2):269-304
A new q-binomial theorem for Macdonald polynomials is employed to prove an A
n
analogue of the celebrated Selberg integral. This confirms the
\mathfrakg = An \mathfrak{g} ={\rm{A}}_{n} case of a conjecture by Mukhin and Varchenko concerning the existence of a Selberg integral for every simple Lie algebra
\mathfrakg \mathfrak{g} . 相似文献
6.
We prove an identity for Hall–Littlewood symmetric functions labelled by the Lie algebra A2. Through specialization this yields a simple proof of the A2 Rogers–Ramanujan identities of Andrews, Schilling and the author. 相似文献
7.
S. O. Warnaar 《Constructive Approximation》2002,18(4):479-502
Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating,
balanced, very-well-poised, elliptic hypergeometric series. 相似文献
8.
George E. Andrews Anne Schilling S. Ole Warnaar 《Journal of the American Mathematical Society》1999,12(3):677-702
Using new -functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A version of the classical Bailey lemma. We apply our result, which is distinct from the A Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W algebra.
9.
We obtain a bijection between certain lattice paths and partitions. This implies a proof of polynomial identities conjectured by Melzer. In a limit, these identities reduce to Rogers-Ramanujantype identities for the
1,1
(p,p+1)
(q) Virasoro characters, conjectured by the Stony Brook group. 相似文献
10.
In a recent letter, new representations were proposed for the pair of sequences (,), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs (,) labelled by the Lie algebra AN – 1, two nonnegative integers and k and a partition , whose parts do not exceed N – 1. Our results give rise to what we call a higher level Bailey lemma. As an application it is shown how this lemma can be applied to yield general q-series identities, which generalize some well-known results of Andrews and Bressoud. 相似文献