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arXiv · 2110.15337

Supercentralizers for deformations of the Pin osp dual pair

Roy Oste
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Abstract

In recent work, we examined the algebraic structure underlying a class of elements supercommuting with realization of the Lie superalgebra $\mathfrak{osp}(1|2)$ inside a generalization of the Weyl Clifford algebra. This generalization contained in particular the deformation by means of Dunkl operators, yielding a rational Cherednik algebra instead of the Weyl algebra. The aim of this work is to show that this is the full supercentralizer, give a (minimal) set of generators, and to describe the relation with the $(\mathrm{Pin}(d),\mathfrak{osp}(2m+1|2n))$ Howe dual pair.

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Roy Oste. 2021-10-28. Supercentralizers for deformations of the Pin osp dual pair. https://arxiv.org/abs/2110.15337

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