English

Pseudo-parabolic category over quaternionic projective plane

Quantum Algebra 2021-10-20 v2 Representation Theory

Abstract

Quaternionic projective plane HP2\mathbb{H} P^2 is the next simplest conjugacy class of the symplectic group SP(6)SP(6) with pseudo-Levi stabilizer subgroup after the sphere S4HP1\mathbb{S}^4\simeq \mathbb{H} P^1. Its quantization gives rise to a module category Ot(HP2)\mathcal{O}_t\bigl(\mathbb{H} P^2\bigr) over finite-dimensional representations of Uq(sp(6))U_q\bigl(\mathfrak{s}\mathfrak{p}(6)\bigr), a full subcategory in the category O\mathcal{O}. We prove that Ot(HP2)\mathcal{O}_t\bigl(\mathbb{H} P^2\bigr) is semi-simple and equaivalent to the category of quantized equivariant vector bundles on HP2\mathbb{H} P^2.

Keywords

Cite

@article{arxiv.1911.10717,
  title  = {Pseudo-parabolic category over quaternionic projective plane},
  author = {Gareth Jones and Andrey Mudrov},
  journal= {arXiv preprint arXiv:1911.10717},
  year   = {2021}
}

Comments

27 pages. A revision of the previous version with improved presentation and more content added. Original results unchanged

R2 v1 2026-06-23T12:25:54.701Z