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Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of A2ℓ−1(2)

  • Liuquan Wang
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Abstract

We prove four conjectures of Takigiku and Tsuchioka consisting of eight Rogers--Ramanujan type identities. Two conjectures involve triple sums and a third involves quadruple sums, and their product sides are certain level $2$ principal characters of A13(2). The fourth conjecture gives multisum representations of certain level $2$ principal characters of A2ℓ−1(2). The proofs rely on the Bailey pair method, finite sum identities involving Gaussian polynomials, and the quintuple product identity.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026proofs,
  title = {{Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of $A_2\ell-1^(2)$}},
  author = {Liuquan Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.18666},
  eprint = {2610.18666},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.18666},
}
RIS
TY  - UNPB
TI  - Proofs of four Takigiku--Tsuchioka conjectures on level $2$ principal characters of A_2ℓ−1^(2)
AU  - Liuquan Wang
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2610.18666
UR  - https://arxiv.org/abs/2610.18666
AB  - We prove four conjectures of Takigiku and Tsuchioka consisting of eight Rogers--Ramanujan type identities. Two conjectures involve triple sums and a third involves quadruple sums, and their product sides are certain level $2$ principal characters of A_13^(2). The fourth conjecture gives multisum representations of certain level $2$ principal characters of A_2ℓ−1^(2). The proofs rely on the Bailey pair method, finite sum identities involving Gaussian polynomials, and the quintuple product identity.
ER  -