2024/09/02 by Aiden Suter, Ben Webster, Suter, Aiden +1
Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Chromodynamics and Particle Interactions #Quantum chaos and dynamical systems #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2409.01379
openalex publication_date 2024/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Remarkable work of Kaledin, based on earlier joint work with Bezrukavnikov, has constructed a tilting generator of the category of coherent sheaves on a very general class of symplectic resolutions of singularities. In this paper, we give a concrete construction of this tilting generator on the cotangent bundle of Gr(2,4), the Grassmannian of 2-planes in ℂ4. This construction builds on work of the second author describing these tilting bundles in terms of KLRW algebras, but in this low-dimensional case, we are able to describe our tilting generator as a sum of geometrically natural bundles on T^*Gr(2,4): line bundles and their extensions, as well as the tautological bundle and its perpendicular.