AN ELLIPTIC BCn BAILEY LEMMA AND ROGERS–RAMANUJAN IDENTITIES ASSOCIATED TO ROOT SYSTEMS
نویسنده
چکیده
(1.2) (a; q)α := (a; q)∞ (aqα; q)∞ in terms of (a; q)∞ := ∏∞ i=0(1− aq ). These identities have a very rich history. Many important figures in mathematics had contributed to the development of these identities starting with Rogers [25] who first proved them in 1894, and Ramanujan [17] whose involvement made Rogers’ unnoticed work popular. Others contributed by simplifying existing proofs, suggesting new proofs of different nature, establishing their relations to other branches of mathematics and generalizing these identities [4], [5], [15], [23], [26], [27]. This paper is devoted to multiple series analogues of the Rogers–Ramanujan identities associated to root systems Bn and Dn of rank n. In §1, the definition of BCn Jackson coefficients, the BCn type symmetric rational function ωλ/μ(z; r, q, p, t; a, b) defined in [8] is reviewed. The cocycle identity
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AN ELLIPTIC BCn BAILEY LEMMA, MULTIPLE ROGERS–RAMANUJAN IDENTITIES AND EULER’S PENTAGONAL NUMBER THEOREMS
An elliptic BCn generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter BCn Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system BCn are proved as applications, including a 6φ5 summation formula, a generalized Watson transformation and an unspecialized Rogers–Selberg identity. The last ...
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