Related papers: The Cayley Grassmannian

The goal of this paper is to better understand a family of linear degenerations of the classical Lagrangian Grassmannians $\Lambda(2n)$. It is the special case for $k=n$ of the varieties $X(k,2n)^{sp}$, introduced in previous joint work…

We unify problems about the equivariant geometry of symmetric quiver representation varieties, in the finite type setting, with the corresponding problems for symmetric varieties $GL(n)/K$ where $K$ is an orthogonal or symplectic group. In…

Let X be a compact almost complex manifold with an action of a finite group G. We compute the algebra of G^n coinvariants of the stringy cohomology (math.AG/0104207) of X^n with an action of a wreath product of G. We show that it is…

We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our…

In this paper, we present a closed formula for the cohomology of real Grassmannians. To achieve this, we use a theory of stratified spaces to compute the differentials in a chain complex that computes the cohomology. Specifically, we…

Let $G$ be a simple algebraic group of type $F_{4}$, $E_{6}$, $E_{7}$ or $E_{8}$, and let $\mathfrak{g}$ be its Lie algebra. The adjoint variety $X_{ad} \subseteq \mathbb{P} \mathfrak{g}$ is defined as the unique closed orbit of the adjoint…

Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X…

This paper explores the structure of bi-Lagrangian Grassmanians for pencils of $2$-forms on real or complex vector spaces. We reduce the analysis to the pencils whose Jordan-Kronecker Canonical Form consists of Jordan blocks with the same…

Let i be a homomorphism of the multiplicative group into a connected reductive algebraic group over C. Let G^i be the centralizer of the image i. Let LG be the Lie algebra of G and let L_nG (n integer) be the summands in the direct sum…

We give a complete description of the bigraded Bredon cohomology ring of smooth projective real quadrics, with coefficients in the constant Mackey functor $ \mathbf{Z} $. These invariants are closely related to the integral motivic…

Let $L$ be a Levi subgroup of $GL_N$ which acts by left multiplication on a Schubert variety $X(w)$ in the Grassmannian $G_{d,N}$. We say that $X(w)$ is a spherical Schubert variety if $X(w)$ is a spherical variety for the action of $L$. In…

Let $ G $ be a connected, simply connected semisimple algebraic group over the complex number field, and let $ K $ be the fixed point subgroup of an involutive automorphism of $ G $ so that $ (G, K) $ is a symmetric pair. We take parabolic…

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G=S_5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.

We compute the equivariant cohomology of complex projective spaces associated to finite-dimensional representations of $C_2$, using ordinary cohomology graded on representations of the fundamental groupoid, with coefficients in the Burnside…

Let k_0 be a field of characteristic 0, and let k be a fixed algebraic closure of k_0. Let G be an algebraic k-group, and let Y be a G-variety over k. Let G_0 be a k_0 -model (k_0 -form) of G. We ask whether Y admits a G_0 -equivariant k_0…

We establish a geometric analog of the Casselman-Shalika formula for a split connected reductive group over a mixed characteristic local field. In particular, we construct sheaves on the Witt vector affine Grassmannian which geometrize the…

Let G be a real, connected, noncompact, semisimple Lie group, let K be a maximal compact subgroup of G, and let g=k+p be the corresponding Cartan decomposition of the complexified Lie algebra of G. Sequences of strongly orthogonal…

We study the topology of compact manifolds with a Lie group action for which there are only finitely many non-principal orbits, and describe the possible orbit spaces which can occur. If some non-principal orbit is singular, we show that…

We classify the smooth projective symmetric G-varieties with Picard number one (and G semisimple). Moreover we prove a criterion for the smoothness of the simple (normal) symmetric varieties whose closed orbit is complete. In particular we…

The Khovanov-Springer variety X(n) is a certain subvariety of the variety of flags of length 2n, which has been studied from various different points of view. We give a new proof of the ring structure of the cohomology of X(n) and relate it…