Some extension algebras for standard modules over KLR algebras of type $A$

Buursma, Doeke; Kleshchev, Alexander; Steinberg, David Joel

doi:10.48550/arxiv.1906.11380

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2021

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“…Some partial results appear appear in [GJ81,Car86]. A similar situation arises for KLR algebras, where resolutions of standard modules can be computed [BKJ21], but the computation of Ext groups appears difficult in general [BKS20]. One of the important and interesting aspects of hypertoric representation theory is that it shares many of the basic structural properties of fundamental categories of Lie theory while remaining significantly less complicated from a computational perspective.…”

Section: Introductionmentioning

confidence: 95%

Strands algebras and the affine highest weight property for equivariant hypertoric categories

Lauda¹,

Licata²,

Manion³

2021

Preprint

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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 [LLM20], this implies a number of new homological results about the bordered Floer algebras of Ozsváth-Szabó, 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-Ozsváth-Thurston bordered strands dg algebras.

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