An Elliptic $BC_n$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems

Hasan Coskun

paper

An Elliptic $B C_{n}$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems

arXiv:math/0605653

Abstract

An elliptic $B C_{n}$ generalization of the classical two parameter Bailey Lemma is proved, and a basic one parameter $B C_{n}$ Bailey Lemma is obtained as a limiting case. Several summation and transformation formulas associated with the root system $B C_{n}$ are proved as applications, including a $_{6} ϕ_{5}$ summation formula, a generalized Watson transformation and an unspecialized Rogers--Selberg identity. The last identity is specialized to give an infinite family of multilateral Rogers--Selberg identities. Standard determinant evaluations are then used to compute $B_{n}$ and $D_{n}$ generalizations of the Rogers--Ramanujan identities in terms of determinants of theta functions. Starting with the $B C_{n}$ $_{6} ϕ_{5}$ summation formula, a similar program is followed to prove an infinite family of $D_{n}$ Euler's Pentagonal Number Theorems.

V2: 36 pages; to appear in AMS Trans; references added; typos corrected

An Elliptic BCn​ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems

Abstract

References in corpus (2)

An Elliptic $B C_{n}$ Bailey Lemma, Multiple Rogers--Ramanujan Identities and Euler's Pentagonal Number Theorems