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Twisted Affine Yangian and Rectangular $W$-algebra of type $D$

· 2021 · math.QA · arXiv 2107.09999

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abstract

We define the twisted affine Yangian of type $C$ and construct surjective homomorphisms from twisted affine Yangians of type $C$ to the universal enveloping algebra of the rectangular $W$-algebra associated with $\mathfrak{so}(ln)$ and a nilpotent element whose Jordan form corresponds to the partition $(l^n)$ in the case when $l$ and $n$ are even.

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  • New presentation of the twisted Yangian of type $D$ math.QA · 2025-07-01 · conditional · none · ref 16 · internal anchor

    A new finite presentation of the twisted Yangian of type D is proven, and a conjectural twisted affine Yangian of type D is defined.