Categorical idempotents via shifted 0-affine algebras. (English) Zbl 07920890
Summary: We show that a categorical action of shifted 0-affine algebra naturally gives two families of pairs of complementary idempotents in the triangulated monoidal category of triangulated endofunctors for each weight category. Consequently, we obtain two families of pairs of complementary idempotents in the triangulated monoidal category \(\mathrm{D}^b \mathrm{Coh}(G/P \times G/P)\). As an application, this provides examples where the projection functors of a semiorthogonal decomposition are kernel functors, and we determine the generators of the component categories in the Grassmannians case.
MSC:
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
| 18N25 | Categorification |
| 20C08 | Hecke algebras and their representations |
| 18F30 | Grothendieck groups (category-theoretic aspects) |
| 18G80 | Derived categories, triangulated categories |
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