2025/04/24 by Maksimau, Ruslan, Minets, Alexandre
#Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2504.17430
We propose an extension of the theory of parity sheaves, which allows for non-locally constant sheaves along strata. Our definition is tailored for proving the existence of (proper, quasihereditary, etc) stratifications of Ext-algebras. We use this to study quiver Schur algebras A(α) for the cyclic quiver of length 2. We find a polynomial quasihereditary structure on A(α) compatible with the categorified PBW basis of McNamara and Kleshchev-Muth, and sharpen their results to arbitrary characteristic. We also prove that semicuspidal algebras of A(nδ) are polynomial quasihereditary covers of semicuspidal algebras of the corresponding KLR algebra R(nδ), and compute them diagrammatically.