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PreprintCC BY 4.0arXiv

Exactness and Drinfeld-Sokolov Realization of the McRae-Yang Tensor Functors

  • Shun Xu
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Abstract

Let p,q≥ 2 be coprime, set k=−2+p/q, k'=−2+q/p, and let cp,q=1−6(p−q)2/(pq). We prove that the McRae--Yang functors Fp,q: KLk(sl2)→𝒪cp,q and Fq,p: KLk'(sl2)→𝒪cp,q are exact and faithful, and, as ℂ-linear functors, are naturally isomorphic to the corresponding principal quantum Drinfeld--Sokolov reductions. Their restrictions to projective objects are fully faithful.

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Cite

BibTeXRIS
BibTeX
@misc{xu2026exactness,
  title = {{Exactness and Drinfeld-Sokolov Realization of the McRae-Yang Tensor Functors}},
  author = {Shun Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.13869},
  eprint = {2608.13869},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.13869},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exactness and Drinfeld-Sokolov Realization of the McRae-Yang Tensor Functors
AU  - Shun Xu
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2608.13869
UR  - https://arxiv.org/abs/2608.13869
AB  - Let p,q≥ 2 be coprime, set k=−2+p/q, k'=−2+q/p, and let c_p,q=1−6(p−q)^2/(pq). We prove that the McRae--Yang functors F_p,q: KL^k(sl_2)→𝒪_c_p,q and F_q,p: KL^k'(sl_2)→𝒪_c_p,q are exact and faithful, and, as ℂ-linear functors, are naturally isomorphic to the corresponding principal quantum Drinfeld--Sokolov reductions. Their restrictions to projective objects are fully faithful.
ER  -