相关论文: B_{n-1}-bundles on the flag variety, II

We show that each orbit of a Borel subgroup $B_{n-1}$ of GL(n-1) (respectively SO(n-1)) on the flag variety of GL(n) (respectively of SO(n)) is a bundle over a $B_{n-1}$-orbit on a generalized flag variety of GL(n-1) (respectively SO(n-1)),…

Let $G=G_{n}=GL(n)$ be the $n\times n$ complex general linear group and embed $G_{n-1}=GL(n-1)$ in the top left hand corner of $G$. The standard Borel subgroup of upper triangular matrices $B_{n-1}$ of $G_{n-1}$ acts on the flag variety of…

Let $G=GL(n)$ be the $n\times n$ complex general linear group and let $\mathcal{B}_{n}$ be its flag variety. The standard Borel subgroup $B$ of upper triangular matrices acts on the product $\mathcal{B}_{n}\times \mathbb{P}^{n-1}$ with…

Let G be a connected reductive complex algebraic group and B a Borel subgroup of G. We consider a subgroup H of B acting with finitely many orbits on the flag variety G/B, and we classify the H-orbits in G/B in terms of suitable…

Let G be the split special orthogonal group of degree 2n+1 over a field F of char F \ne 2. Then we describe G-orbits on the triple flag varieties G/P\times G/P\times G/P and G/P\times G/P\times G/B with respect to the diagonal action of G…

We give a new construction of the Bott-Samelson variety $Z$ as the closure of a $B$-orbit in a product of flag varieties $(G/B)^l$. This also gives an embedding of the projective coordinate ring of the variety into the function ring of a…

Let $G$ be a connected reductive algebraic group over an algebraically closed field ${\bf k}$ of characteristic not equal to 2, let $\B$ be the variety of all Borel subgroups of $G$, and let $K$ be a symmetric subgroup of $G$. Fixing a…

Motivated by branching problems for principal series representations of the Lie group $G = GL(n,\mathbb R)$, we consider all pairs $(G', P)$ with $G'$ being the Levy factor of a parabolic subgroup of $G$ and $P$ a parabolic subgroup of $G$…

Let $G$ be a quasi-simple algebraic group defined over an algebraically closed field $k$ and $B$ a Borel subgroup of $G$ acting on the nilradical $\mathfrak{n}$ of its Lie algebra $\mathfrak{b}$ via the Adjoint representation. It is known…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of GL_n(C) on the variety of x-nilpotent complex matrices. We obtain a criterion as to whether the action admits a finite number of orbits and specify a…

Let $G$ be a quasi-simple algebraic group defined over an algebraically closed field $k$ and $B$ a Borel subgroup of $G$ acting on the nilradical $\mathfrak{n}$ of its Lie algebra $\mathfrak{b}$ via the Adjoint representation. It is known…

Problem: Given a reductive algebraic group G, find all k-tuples of parabolic subgroups (P_1,...,P_k) such that the product of flag varieties G/P_1 x ... x G/P_k has finitely many orbits under the diagonal action of G. In this case we call…

Let $SP_n(\mathbb{C})$ be the symplectic group and $\mathfrak{sp}_n(\mathbb{C})$ its Lie algebra. Let $B$ be a Borel subgroup of $SP_n(\mathbb{C} )$, $\mathfrak{b}={\rm Lie}(B)$ and $\mathfrak n$ its nilradical. Let $\mathcal X$ be a…

Let $ G $ be a connected reductive algebraic group over $ \mathbb{R} $, and $ H $ its symmetric subgroup. For parabolic subgroups $ P_{G} \subset G $ and $ P_{H} \subset H $, the product of flag varieties $ \mathfrak{X} = H/P_H \times G/P_G…

Let F be the flag variety of a complex semi-simple group G, let H be an algebraic subgroup of G acting on F with finitely many orbits, and let V be an H-orbit closure in F. Expanding the cohomology class of V in the basis of Schubert…

A real form $G_0$ of a complex semisimple Lie group $G$ has only finitely many orbits in any given compact $G$-homogeneous projective algebraic manifold $Z=G/Q$. A maximal compact subgroup $K_0$ of $G_0$ has special orbits $C$ which are…

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…

This is a continuation of our combinatorial program on the enumeration of Borel orbits in symmetric varieties of classical types. Here, we determine the generating series the numbers of Borel orbits in…

The main result of this paper is a new parameterization of the orbits of a symmetric subgroup on a partial flag variety. The parameterization is in terms of certain Spaltenstein varieties, on one hand, and certain nilpotent orbits, on the…

We construct two families of representations of the braid group $B_n$ by considering conjugation actions on congruence subgroups of $GL_{n-1}(Z[t^{\pm 1},q^{\pm 1}])$. We show that many of these representations are faithful modulo the…