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PreprintCC BY 4.0arXiv

Character recurrences and level one formulas for B2(1)

  • Miroslav Jerkovic
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Abstract

We obtain recurrence relations for formal characters of Feigin-Stoyanovsky type subspaces of standard B2(1)-modules at fixed level. The recurrences are derived directly from the combinatorial bases described by difference and initial conditions. Unlike in type Aℓ(1), the right side in general involves several shifted characters. We give explicit polynomial coefficients and prove that the resulting system, together with the constant term normalization, determines all formal characters at fixed level uniquely. At level $1$ we solve the recurrence system explicitly and obtain fermionic formulas for all three characters. We also relate these characters to the multigraded generating functions for exponent triples parametrizing the Meurman-Primc monomial basis of standard A1(1)-modules.

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Cite

BibTeXRIS
BibTeX
@misc{jerkovic2026character,
  title = {{Character recurrences and level one formulas for $B_2^(1)$}},
  author = {Miroslav Jerkovic},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08251},
  eprint = {2610.08251},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08251},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Character recurrences and level one formulas for B_2^(1)
AU  - Miroslav Jerkovic
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2610.08251
UR  - https://arxiv.org/abs/2610.08251
AB  - We obtain recurrence relations for formal characters of Feigin-Stoyanovsky type subspaces of standard B_2^(1)-modules at fixed level. The recurrences are derived directly from the combinatorial bases described by difference and initial conditions. Unlike in type A_ℓ^(1), the right side in general involves several shifted characters. We give explicit polynomial coefficients and prove that the resulting system, together with the constant term normalization, determines all formal characters at fixed level uniquely. At level $1$ we solve the recurrence system explicitly and obtain fermionic formulas for all three characters. We also relate these characters to the multigraded generating functions for exponent triples parametrizing the Meurman-Primc monomial basis of standard A_1^(1)-modules.
ER  -