A Higher-Level Bailey Lemma
نویسندگان
چکیده
منابع مشابه
A Higher-level Bailey Lemma
We propose a generalization of Bailey’s lemma, useful for proving q-series identities. As an application, generalizations of Euler’s identity, the Rogers–Ramanujan identities, and the Andrews–Gordon identities are derived. The generalized Bailey lemma also allows one to derive the branching functions of higher-level A (1) 1 cosets. 1. The Bailey Lemma In his famous 1949 paper, W. N. Bailey note...
متن کاملA Higher-Level Bailey Lemma: Proof and Application
In a recent letter, a “higher-level” generalization of Bailey’s lemma was proposed. Here we extend and prove this result. In particular we provide new representations for the pair of sequences (γ, δ) as defined by Bailey in his celebrated lemma. These representations are labelled by the Lie algebra AN−1, two non-negative integers l and k and a partition λ, whose parts do not exceed N − 1. As an...
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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 n−1 and to identities for A-type branching functions.
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An elementary introduction to the recently introduced A2 Bailey lemma for supernomial coefficients is presented. As illustration, some A2 q-series identities are (re)derived which are natural analogues of the classical (A1) Rogers–Ramanujan identities and their generalizations of Andrews and Bressoud. The intimately related, but unsolved problems of supernomial inversion, An−1 and higher level ...
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for |q| < 1. The fame of these identities lies not only in their beauty and fascinating history [17, 3], but also in their relevance to the theory of partitions and many other branches of mathematics and physics. In particular, MacMahon [27] and Schur [39] independently noted that the left-hand side of (1.1) is the generating function for partitions into parts with difference at least two, whil...
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ژورنال
عنوان ژورنال: International Journal of Modern Physics B
سال: 1997
ISSN: 0217-9792,1793-6578
DOI: 10.1142/s0217979297000253