Minuscule embeddings

Minuscule Representations

K-theory of Minuscule Varieties

Based on Thomas and Yong’s K-theoretic jeu de taquin algorithm, we prove a uniform Littlewood-Richardson rule for the K-theoretic Schubert structure constants of all minuscule homogeneous spaces. Our formula is new in all types. For the main examples of Grassmannians of type A and maximal orthogonal Grassmannians it has the advantage that the tableaux to be counted can be recognized without ref...

Minuscule Elements of Weyl Groups

Minuscule Schubert Varieties and Mirror Symmetry

We consider smooth complete intersection Calabi–Yau 3-folds in minuscule Schubert varieties, and study their mirror symmetry by degenerating the ambient Schubert varieties to Hibi toric varieties. We list all possible Calabi–Yau 3-folds of this type up to deformation equivalences, and find a new example of smooth Calabi–Yau 3-folds of Picard number one; a complete intersection in a locally fact...

Rational Curves on Minuscule Schubert Varieties

Let us denote by C the variety of lines in P3 meeting a fixed line, it is a grassmannian (and hence minuscule) Schubert variety. In [P2] we described the irreducible components of the scheme of morphisms from P1 to C and the general morphism of these irreducible components. In this text we study the scheme of morphisms from P1 to any minuscule Schubert variety X. Let us recall that we studied i...