Related papers: On orbits in double flag varieties for symmetric p…

This thesis studies the symplectic structure of holomorphic coadjoint orbits, and their projections. A holomorphic coadjoint orbit O is an elliptic coadjoint orbit which is endowed with a natural invariant K\"ahlerian structure. These…

A two-orbit variety is a normal complete complex algebraic variety on which a reductive complex algebraic group acts with exactly two orbits. The aim of this paper is to give the classification of all two-orbit varieties and to prove Luna's…

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…

The flag variety of a complex reductive linear algebraic group G is by definition the quotient G/B by a Borel subgroup. It can be regarded as the set of Borel subalgebras of Lie(G). Given a nilpotent element e in Lie(G), one calls Springer…

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…

We quantize the problem considered by Bott-Samelson who applied Morse theory to any compact symmetric space $G/K$ and the associated real flag manifold $G_{\mathbb{R}}/B$ which is a real locus of a complex partial flag variety…

Let G be a connected reductive group. Recall that a G-variety X is called spherical if X is normal and a Borel subgroup of G has an open orbit on X. To a spherical homogeneous G-space one assigns certain combinatorial invariants: the weight…

We introduce quantum super-spherical pairs as coideal subalgebras in general linear and orthosymplectic quantum supergroups. These subalgebras play a role of isotropy subgroups for matrices solving $\mathbb{Z}_2$-graded reflection equation.…

We characterize the Sp_{2n} orbits in the flag variety for SL_{2n} with rationally smooth closure via a pattern avoidance criterion, also showing that the singular and rationally singular loci of such orbit closures coincide.

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type $A_{n-1}$. This is obtained inside the limit of a projective system of Borel-Moore homologies of…

A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…

We describe the action of the Weyl group of a semi simple linear group $G$ on cohomological and K-theoretic invariants of the generalized flag variety $G/B$. We study the automorphism $s_i$, induced by the reflection in the simple root, on…

Let $G$ be a complex reductive group and $P$ be a parabolic subgroup of $G$. In this paper the authors address questions involving the realization of the $G$-module of the global sections of the (twisted) cotangent bundle over the flag…

Let $K$ be a finite group and let $G$ be a finite group acting on $K$ by automorphisms. In this paper we study two different but intimately related subjects: on the one side we classify all possible multiplicative and associative structures…

Let $G$ be a complex simple direct limit group, specifically $SL(\infty;\mathbb{C})$, $SO(\infty;\mathbb{C})$ or $Sp(\infty;\mathbb{C})$. Let $\mathcal{F}$ be a (generalized) flag in $\mathbb{C}^\infty$. If $G$ is $SO(\infty;\mathbb{C})$ or…

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each K_C-orbit S on every flag manifold G_C/P and conjectured that the connected component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain D if S is of…

We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen-Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry,…

Let G be a connected semisimple complex algebraic group and let P be a parabolic subgroup. In this paper we define a new (commutative and associative) product on the cohomology of the homogenous spaces G/P and use this to give a more…

If $K$ is a closed subgroup of a compact group $G$, the probability that randomly chosen pair of elements from $K$ and $G$ commute is denoted by $Pr(K,G)$. Say that a subgroup $K\leq G$ is $\epsilon$-central in $G$ if $Pr(\langle g…