Related papers: Orbital varieties in type $D$

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

In this paper we define an action of the Weyl group on the quiver varieties $M_{m,\grl}(d,v)$ with generic $(m,\grl)$. To do it we describe a set of generators of the projective ring of a quiver variety. We also prove connectness for the…

This paper concerns a class of orbital integrals in Lie algebras over p-adic fields. The values of these orbital integrals at the unit element in the Hecke algebra count points on varieties over finite fields. The construction, which is…

We prove that varieties are uniquely determined by the derived category of $\mathscr{O}[[\hbar]]$-modules with coherent cohomology which is the same as $\mathscr{O}$-modules proved by A. Bondal and D. Orlov. We also generalize a theorem of…

We consider the conjugation-action of the Borel subgroup of the symplectic or the orthogonal group on the variety of nilpotent complex elements of nilpotency degree $2$ in its Lie algebra. We translate the setup to a…

We investigate weight modules for finite and infinite Weyl algebras, classifying all such simple modules. We also study the representation type of the blocks of locally-finite weight module categories and describe indecomposable modules in…

Let $\mathfrak{g}$ be a simple Lie algebra defined over an algebraically closed field $k$ of characteristic $p$. Fix an integer $r>1$ and suppose that $V_1,\ldots,V_r$ are irreducible closed subvarieties of $\mathfrak{g}$. Let…

Trialitarian automorphisms are related to automorphisms of order 3 of the Dynkin diagram of type D4. Octic etale algebras with trivial discriminant, containing quartic subalgebras, are classified by Galois cohomology with value in the Weyl…

We classify the pairs $(A,D)$ consisting of an $(\epsilon,\Gamma)$-olor-commutative associative algebra $A$ with an identity element over an algebraically closed field $F$ of characteristic zero and a finite dimensional subspace $D$ of…

We describe algorithms for computing the induced nilpotent orbits in semisimple Lie algebras. We use them to obtain the induction tables for the Lie algebras of exceptional type. This also yields the classification of the rigid nilpotent…

For finite Lie algebras, it is shown that characters can be defined first for Weyl orbits and then for irreducible representations. For $A_N$ Lie algebras, weight multiplicities can then be calculated by only stating that characters are…

Recursive algebraic construction of two infinite families of polynomials in $n$ variables is proposed as a uniform method applicable to every semisimple Lie group of rank $n$. Its result recognizes Chebyshev polynomials of the first and…

We give a geometric description of the blocks of the Brauer algebra $B_n(\delta)$ in characteristic zero as orbits of the Weyl group of type $D_n$. We show how the corresponding affine Weyl group controls the representation theory of the…

We give an easy diagrammatical description of the parabolic Kazhdan-Lusztig polynomials for the Weyl group $W_n$ of type $D_n$ with parabolic subgroup of type $A_n$ and consequently an explicit counting formula for the dimension of the…

We study a graded algebra D=D(L,G) defined by a finite lattice L and a subset G in L, a so-called building set. This algebra is a generalization of the cohomology algebras of hyperplane arrangement compactifications found in work of De…

We study families of algebraic varieties parametrized by topological spaces and generalize some classical results such as Hilbert Nullstellensatz and primary decomposition of commutative rings. We show that there is an equivalence between…

Four types of discrete transforms of Weyl orbit functions on the finite point sets are developed. The point sets are formed by intersections of the dual-root lattices with the fundamental domains of the affine Weyl groups. The finite sets…

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is given by the source vertical tangent bundle restricted to the identity bisection. Its sections can be identified with the invariant vector…

In this paper we improve our previous results on classification of groups of points on abelian varieties over finite fields. The classification is given in terms of the Weil polynomial of abelian varieties in a given $k$-isogeny class.

Let G be a simple algebraic group over an algebraically closed field with Lie algebra g. Then the orbits of nilpotent elements of g under the adjoint action of G have been classified. We describe a simple algorithm for finding a…