Related papers: Classification of double flag varieties of complex…

A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…

A 2-category was introduced in arXiv:0803.3652 [math.QA] that categorifies Lusztig's integral version of quantum sl(2). Here we construct for each positive integer N arepresentation of this 2-category using the equivariant cohomology of…

In this paper we prove that the category of parity complexes on the flag variety of a complex connected reductive group is a "graded version" of the category of tilting perverse sheaves on the flag variety of the dual group, for any field…

We classify all products of flag varieties with finitely many orbits under the diagonal action of the general linear group. We also classify the orbits in each case and construct explicit representatives. This generalizes the classical…

We define a variety of doubly indexed flags, this is a smooth, projective variety, and we describe it as an iterated over Grassmannian varieties. On the other hand, we consider the variety of partial flags which are stabilized by a given…

This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.

We compute the Hilbert series of general weighted flag varieties and discuss a computer-aided method to determine their defining equations. We apply our results to weighted flag varieties coming from the Lie groups of type G_2 and GL(6), to…

For a connected semisimple algebraic group $G$, we consider some special infinite series of tensor products of simple $G$-modules whose $G$-fixed point spaces are at most one-dimensional. We prove that their existence is closely related to…

For semisimple Lie superalgebras over an algebraically closed field of characteristic zero, whose category of finite dimensional super representations is semisismple, we classify all irreducible super representations for which the…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We investigate the Ulrich complexity of certain examples of Brauer--Severi varieties, twisted flags and involution varieties and establish lower and upper bounds. Furthermore, we relate Ulrich complexity to the categorical representability…

Let $ G $ be a connected reductive algebraic group and its symmetric subgroup $ K $. The variety $ \dblFV = K/Q \times G/P $ is called a double flag variety, where $ Q $ and $ P $ are parabolic subgroups of $ K $ and $ G $ respectively. In…

The flag type of a semigroup S of a noncompact semisimple Lie group is an algebraic tool related to the geometry of the invariant control set determined by S on the flag manifolds of G. In the present paper we show that it is possible to…

This paper introduces a two-parameter deformation of the cohomology of generalized flag varieties. One special case is the Belkale-Kumar deformation (used to study eigencones of Lie groups). Another picks out intersections of Schubert…

We study subvarieties of the flag variety called Hessenberg varieties, defined by certain linear conditions. These subvarieties arise naturally in applications including geometric representation theory, number theory, and numerical…

The Lie algbera of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

We show that in type A or C any degenerate flag variety is in fact isomorphic to a Schubert variety in an appropriate partial flag manifold.

We determine the set of supports for the flat family of linear degenerations of flag varieties in terms of Motzkin combinatorics.