Affiliation:
1. Massachusetts Institute of Technology, Mathematics
Abstract
Abstract
In this paper, we give an alternative construction of a certain class of deformed double current algebras. These algebras are deformations of $ U(\textrm {End}(\Bbbk ^r)[x,y]) $ and they were initially defined and studied by N. Guay in his papers. Here, we construct them as algebras of endomorphisms in Deligne category. We do this by taking an ultraproduct of spherical subalgebras of the extended Cherednik algebras of finite rank.
Publisher
Oxford University Press (OUP)
Reference21 articles.
1. On blocks of Deligne’s category $\textrm {Rep}(S_t)$;Comes;Adv. Math.,2011
2. On Deligne’s category $\textrm {Rep}^{ab} (S_d)$;Comes;Algebra Number Theory,2014
3. Holography and Koszul duality: the example of the $M_2$ brane;Costello,2017
4. Deligne’s category $\textrm {Rep}(GL_{\delta })$ and representations of general linear supergroups;Comes;Represent. Theory,2012
5. La catégorie des représentations du groupe symétrique ${S}_t$, lorsque t n’est pas un entier naturel;Deligne;Tata Inst. Fundam. Res. Publ.,2007