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arXiv · 2001.00073

The nil-blob algebra: An incarnation of type $\tilde{A}_1$ Soergel calculus and of the truncated blob algebra

Diego Lobos·David Plaza·Steen Ryom-Hansen
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Abstract

We introduce a type $B$ analogue of the nil Temperley-Lieb algebra in terms of generators and relations, that we call the (extended) nil-blob algebra. We show that this algebra is isomorphic to the endomorphism algebra of a Bott-Samelson bimodule in type $\tilde{A}_1$. We also prove that it is isomorphic to an idempotent truncation of the classical blob algebra.Thus we provide strong evidence in favor of the recent Blob vs. Soergel conjecture.

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Diego Lobos, David Plaza, Steen Ryom-Hansen. 2020-12-05. The nil-blob algebra: An incarnation of type $\tilde{A}_1$ Soergel calculus and of the truncated blob algebra. https://arxiv.org/abs/2001.00073

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