Tootfinder

Weight modules and gluing of sheaves on the flag variety
Pablo Boixeda Alvarez, Calder Morton-Ferguson
https://arxiv.org/abs/2509.25156 https://arxiv.org/p…

Weight modules and gluing of sheaves on the flag variety
We study a natural enlargement of the BGG Category O for a semisimple Lie algebra: the category of weight modules with trivial central character and finite-dimensional weight spaces supported on the root lattice. We give a geometric realization of this category as unipotently monodromic sheaves on the flag variety satisfying a singular support condition. We then explain that a derived version $\mathcal{D}$ of this category is Koszul dual to the Kazhdan-Laumon Category O, a different enlargement…

Semisimple module categories with fusion rules of the compact full flag manifold type
Mao Hoshino
https://arxiv.org/abs/2510.12057 https://arxiv.org/pdf/25…

Semisimple module categories with fusion rules of the compact full flag manifold type
We classify semisimple left module categories over the representation category of a type A quantum group whose fusion rules arise from the maximal torus. The classification is connected to equivariant Poisson structures on compact full flag manifolds in the operator-algebraic setting, and on semisimple coadjoint orbits in the algebraic setting. We also provide an explicit construction based on the BGG categories of deformed quantum enveloping algebras, whose unitarizability corresponds to being…

Special Lagrangian sections and stability conditions on threefolds
Jacopo Stoppa
https://arxiv.org/abs/2508.17709 https://arxiv.org/pdf/2508.17709

Special Lagrangian sections and stability conditions on threefolds
We study a class of Lagrangian submanifolds, given by sections of a special Lagrangian fibration, contained in certain almost Calabi-Yau threefolds (mirrors of polarised toric threefolds satisfying suitable assumptions). We show that, for a Lagrangian section $L$ in this class, the shift $L[2]$ defines an object in the heart of a natural Bridgeland stability condition on the relevant Fukaya-Seidel category, and that if $L[2]$ is semistable with respect to this stability condition, then it is is…

On the geometric Satake equivalence for Kac-Moody groups
Alexis Bouthier, Eric Vasserot
https://arxiv.org/abs/2510.11466 https://arxiv.org/pdf/2510.11466…

On the geometric Satake equivalence for Kac-Moody groups
This article establishes a geometric Satake equivalence for affine Kac-Moody groups as an equivalence of abelian semisimple categories over algebraically closed fields. We define a well-behaved category of equivariant sheaves on the double affine grassmannian \Gr_{G}, seen as a infty-stack, that we equip with a t-structure. We obtain an Braden's hyperbolic localization theorem for such a stack and prove that the constant term functor is t-exact using dimension estimates for affine MV-cycles. We…