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PreprintCC BY 4.0arXiv

Clifford BMW Categories and Conformal Embeddings of Types B C and D

  • August Bergquist
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Abstract

In this paper, we give diagrammatic descriptions of the quantum subgroups coming from conformal embeddings of the form 𝒱(g), checkh) βŠ‚ 𝒱(sodim g, 1) for g∈ {soN, sp2N}, as well as the conformal embeddings of the form 𝒱(sp2r + 2, 2r) βŠ‚ π’ž(sodim sp2r + 2, 1), extending the techniques of Edie-Michell and Snyder which applied to conformal embeddings of the form 𝒱(slr, r) βŠ‚ 𝒱(sodim slr, 1). Our main conceptual innovation is the use of fermion condensation to construct a continuous family of planar superalgebras, which we call the Clifford BMW supercategories. The tower of endomorphism algebras, CWn(Οƒ, Ξ΅) is a combination of Birman Wenzl Murakami algebras and Clifford algebras, much in the spirit of the Hecke Clifford algebras. This tower of algebras appears to be new, and already yields some exciting combinatorics.

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Cite

BibTeXRIS
BibTeX
@misc{bergquist2026clifford,
  title = {{Clifford BMW Categories and Conformal Embeddings of Types B C and D}},
  author = {August Bergquist},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07221},
  eprint = {2611.07221},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07221},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Clifford BMW Categories and Conformal Embeddings of Types B C and D
AU  - August Bergquist
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07221
UR  - https://arxiv.org/abs/2611.07221
AB  - In this paper, we give diagrammatic descriptions of the quantum subgroups coming from conformal embeddings of the form 𝒱(g), checkh) βŠ‚ 𝒱(so_dim g, 1) for g∈ {so_N, sp_2N}, as well as the conformal embeddings of the form 𝒱(sp_2r + 2, 2r) βŠ‚ π’ž(so_dim sp_2r + 2, 1), extending the techniques of Edie-Michell and Snyder which applied to conformal embeddings of the form 𝒱(sl_r, r) βŠ‚ 𝒱(so_dim sl_r, 1). Our main conceptual innovation is the use of fermion condensation to construct a continuous family of planar superalgebras, which we call the Clifford BMW supercategories. The tower of endomorphism algebras, CW_n(Οƒ, Ξ΅) is a combination of Birman Wenzl Murakami algebras and Clifford algebras, much in the spirit of the Hecke Clifford algebras. This tower of algebras appears to be new, and already yields some exciting combinatorics.
ER  -