Exceptional collections on isotropic Grassmannians (Q268591)

Let \(\mathcal{T}\) be an algebraic triangulated category. A sequence of objects \(E_1, \hdots, E_n \in \mathcal{T}\) is called an exceptional sequence if \(\mathsf{Ext}^l(E_i,E_i)\cong \delta_{0,l}K\) for all \(i\) and if there are no morphisms from \(E_i[k]\) to \(E_j\) for any \(i > j\). An exceptional collection is of expected length, if \(n\) is equal to the rank of the Grothendieck group \(K_0(\mathcal{T})\).NEWLINENEWLINEFollowing \textit{M. M. Kapranov}'s result [Invent. Math. 92, No. 3, 479--508 (1988; Zbl 0651.18008)] that the bounded derived category of coherent sheaves on Grassmannian admits exceptional collections of expected length, one may wonder whether the same holds true for any derived category of coherent sheaves on \(G/P\), where \(G\) is a semisimple algebraic group and \(P \subseteq G\) is a parabolic subgroup.NEWLINENEWLINEIn the article under review the authors construct exceptional collections of expected length for the derived category of coherent sheaves on \(G/P\), where \(G\) is simple of type \(B_n\), \(C_n\) or \(D_n\) and \(P \subseteq G\) is a parabolic subgroup.