An $\mathrm{A}_{2}$ Bailey tree and $\mathrm{A}_{2}^{(1)}$ Rogers–Ramanujan-type identities
Year: 2025
Type: article
Abstract: The \mathrm{A}_{2} Bailey chain of Andrews, Schilling and the author is extended to a four-parameter \mathrm{A}_{2} Bailey tree. As main application of this tree, we prove the Kanade–Russell conjecture for a three-parameter family of Rogers–Ramanujan-type identities related to the principal characters of the affine Lie algebra \mathrm{A}_{2}^{(1)} . Combined with known q -series results, this further implies an \mathrm{A}_{2}^{(1)} -analogue of the celebrated Andrews–Gordon q -series identities. We also use the \mathrm{A}_{2} Bailey tree to prove a Rogers–Selberg-type identity for the characters of the principal subspaces of \mathrm{A}_{2}^{(1)} indexed by arbitrary level- k dominant integral weights \lambda . This generalises a result of Feigin, Feigin, Jimbo, Miwa and Mukhin for \lambda=k\Lambda_{0} .
DOI: 10.4171/jems/1627
Author: S. Ole Warnaar
Institution: The University of Queensland
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4409410828