A-D-E POLYNOMIAL AND ROGERS-RAMANUJAN IDENTITIES
نویسندگان
چکیده
منابع مشابه
A-D-E Polynomial and Rogers–Ramanujan Identities
We conjecture polynomial identities which imply Rogers–Ramanujan type identities for branching functions associated with the cosets (G)l−1⊗(G )1/(G )l, with G=An−1 (l ≥ 2), Dn−1 (l ≥ 2), E6,7,8 (l = 2). In support of our conjectures we establish the correct behaviour under level-rank duality for G=An−1 and show that the A-D-E Rogers–Ramanujan identities have the expected q → 1− asymptotics in t...
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We present two general finite extensions for each of the two Rogers-Ramanujan identities. Of these one can be derived directly from Watson’s transformation formula by specialization or through Bailey’s method, the second similar formula can be proved either by using the first formula and the q-Gosper algorithm, or through the so-called Bailey lattice.
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Polynomial generalizations of all 130 of the identities in Slater’s list of identities of the Rogers-Ramanujan type are presented. Furthermore, duality relationships among many of the identities are derived. Some of the these polynomial identities were previously known but many are new. The author has implemented much of the finitization process in a Maple package which is available for free do...
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Abstract. We extend partition-theoretic work of Andrews, Bressoud, and Burge to overpartitions, defining the notions of successive ranks, generalized Durfee squares, and generalized lattice paths, and then relating these to overpartitions defined by multiplicity conditions on the parts. This leads to many new partition and overpartition identities, and provides a unification of a number of well...
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We evaluate several integrals involving generating functions of continuous q-Hermite polynomials in two diierent ways. The resulting identities give new proofs and generalizations of the Rogers-Ramanujan identities. Two quintic transformations are given, one of which immediately proves the Rogers-Ramanujan identities without the Jacobi triple product identity. Similar techniques lead to new tra...
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ژورنال
عنوان ژورنال: International Journal of Modern Physics A
سال: 1996
ISSN: 0217-751X,1793-656X
DOI: 10.1142/s0217751x96000146