Unitary grassmannians

Unitary Grassmannians

We study projective homogeneous varieties under an action of a projective unitary group (of outer type). We are especially interested in the case of (unitary) grassmannians of totally isotropic subspaces of a hermitian form over a field, the main result saying that these grassmannians are 2-incompressible if the hermitian form is generic. Applications to orthogonal grassmannians are provided.

Unitary Grassmannians of Division Algebras

We consider a central division algebra over a separable quadratic extension of a base field endowed with a unitary involution and prove 2-incompressibility of certain varieties of isotropic right ideals of the algebra. The remaining related projective homogeneous varieties are shown to be 2-compressible in general. Together with [17], where a similar issue for orthogonal and symplectic involuti...

A survey of symmetric functions, Grassmannians, and representations of the unitary group

Weighted Grassmannians

Many classes of projective algebraic varieties can be studied in terms of graded rings. Gorenstein graded rings in small codimension have been studied recently from an algebraic point of view, but the geometric meaning of the resulting structures is still relatively poorly understood. We discuss here the weighted projective analogs of homogeneous spaces such as the Grassmannian Gr(2, 5) and ort...

Combinatorial Grassmannians

We follow the rules: k, n denote elements of N and X, Y , Z denote sets. One can prove the following propositions: (1) For all sets a, b such that a 6= b and a = n and b = n holds a ∩ b < n and n+ 1 ≤ a ∪ b. (2) For all sets a, b such that a = n+ k and b = n+ k holds a ∩ b = n iff a ∪ b = n+ 2 · k. (3) X ≤ Y iff there exists a function f such that f is one-to-one and X ⊆ dom f and f ◦X ⊆ Y. (4)...