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Reduction Algebras Involving Symplectic Lie Algebras

  • Dustin Baker
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Abstract

A complete presentation for the diagonal reduction algebra of gln was found by Khoroshkin and Ogievetsky. In this paper we present a complete set of ordering relations for a reduction algebra ℬn associated to gln in a parabolic subalgebra of sp2n. We also study its connection to the diagonal reduction algebra of sp2n. We use braid group action by Zhelobenko automorphisms to reduce the computations required. Another important tool we employ is the ABRR equation for the extremal projector. As an application we prove that all homogeneous ordering relations for the diagonal reduction algebra of sp2n are obtained from the relations in ℬn by applying type Cn Zhelobenko automorphisms.

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Cite

BibTeXRIS
BibTeX
@misc{baker2026reduction,
  title = {{Reduction Algebras Involving Symplectic Lie Algebras}},
  author = {Dustin Baker},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27116},
  eprint = {2609.27116},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27116},
}
RIS
TY  - UNPB
TI  - Reduction Algebras Involving Symplectic Lie Algebras
AU  - Dustin Baker
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.27116
UR  - https://arxiv.org/abs/2609.27116
AB  - A complete presentation for the diagonal reduction algebra of gl_n was found by Khoroshkin and Ogievetsky. In this paper we present a complete set of ordering relations for a reduction algebra ℬ_n associated to gl_n in a parabolic subalgebra of sp_2n. We also study its connection to the diagonal reduction algebra of sp_2n. We use braid group action by Zhelobenko automorphisms to reduce the computations required. Another important tool we employ is the ABRR equation for the extremal projector. As an application we prove that all homogeneous ordering relations for the diagonal reduction algebra of sp_2n are obtained from the relations in ℬ_n by applying type C_n Zhelobenko automorphisms.
ER  -