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We show that the equivariant hypertoric convolution algebras introduced by Braden-Licata-Proudfoot-Webster are affine quasi hereditary in the sense of Kleshchev and compute the Ext groups between standard modules. Together with the main result of arXiv:2009.03981, this implies a number of new homological results about the bordered Floer algebras of Ozsvath-Szabo, including the existence of standard modules over these algebras. We prove that the Ext groups between standard modules are isomorphic to the homology of a variant of the Lipshitz-Ozsvath-Thurston bordered strands dg algebras.
For a Dynkin quiver $Q$ (of type ADE), we consider a central completion of the convolution algebra of the equivariant K-group of a certain Steinberg type graded quiver variety. We observe that it is affine quasi-hereditary and prove that its category
In 2006, Gao and Zeng cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we construct a clas
We study the relation between quantum affine algebras of type A and Grassmannian cluster algebras. Hernandez and Leclerc described an isomorphism from the Grothendieck ring of a certain subcategory $mathcal{C}_{ell}$ of $U_q(hat{mathfrak{sl}_n})$-mod
We prove a character formula for the irreducible modules from the category $mathcal{O}$ over the simple affine vertex algebra of type $A_n$ and $C_n$ $(n geq 2)$ of level $k=-1$. We also give a conjectured character formula for types $D_4$, $E_6$, $E
We discuss the structure of the Motzkin algebra $M_k(D)$ by introducing a sequence of idempotents and the basic construction. We show that $cup_{kgeq 1}M_k(D)$ admits a factor trace if and only if $Din {2cos(pi/n)+1|ngeq 3}cup [3,infty)$ and higher c