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In this article, we show that the categorical action of the shifted $q=0$affine algebra can be used to construct (or induce) t-structures on the weightcategories. The main idea is to interpret the exceptional collectionconstructed by Kapranov as convolution of Fourier-Mukai kernels in thecategorical action via using the Borel-Weil-Bott theorem.  In particular, when the categories are the bounded derived category ofcoherent sheaves on Grassmannians. The t-structure we obtain is precisely theexotic t-structure defined by Bezrukavnikov of the exceptional collectionsgiven by Kapranov. As an application, we calculate the matrix coefficients forgenerators of the shifted $q=0$ affine algebra on the basis given by Kapranovexceptional collections.

Exceptional collections, t-structures, and categorical action of shifted $q=0$ affine algebra, $\mathfrak{sl}_{2}$ case