相关论文: Branching rules for the Weyl group orbits of the L…

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…

Super Weyl group plays an important role in the study of representations of basic classical Lie superalgebras. The Coxeter graphs for super Weyl groups of basis classical Lie superalgebras have been given in \cite{CLS}, where the authors…

Let $(V,\gamma )$ be a real finite dimensional vector space with a symmetric bilinear form $\gamma $ whose kernel is spanned by a nonzero vector. The set of invertible real linear mappings of $(V, \gamma )$ into itself forms a Lie group…

Dynkin's classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to linear Lie superalgebras. Namely, the maximal non-simple irreducible subalgebras of $\mathfrak{gl}(p|q), \mathfrak{q}(n),…

We give an apriori description of a set of irreducible representations of a Weyl group which parametrize the nilpotent orbits in the Lie algebra of a connected reductive group in arbitrary characteristic. We also answer a question of Serre…

Separable elements in Weyl groups are generalizations of the well-known class of separable permutations in symmetric groups. Gaetz and Gao showed that for any pair $(X,Y)$ of subsets of the symmetric group $\mathfrak{S}_n$, the…

We formulate and prove that there are "abundant" in nilpotent orbits in real semisimple Lie algebras, in the following sense. If S denotes the collection of hyperbolic elements corresponding the weighted Dynkin diagrams coming from…

Let $G$ be a reductive group with Borel $B$ and Weyl group $W$. Then $B$-double cosets in $G$ are indexed by the Weyl group, say $O(w)$ for $w\in W$. Then we prove the minimal $B$-double coset in the convolution $O(w_1)*O(w_2)$ is…

For the two Cartan type S subalgebras of the Witt algebra $\W_n$, called Lie algebras of divergence-zero vector fields, we determine all module structures on the universal enveloping algebra of their Cartan subalgebra $\h_n$. We also give…

We give a complete classification of the class of Lie algebras of simply connected real Lie groups whose nontrivial coadjoint orbits are of codimension 1. Such a Lie group belongs to a well-known class, called the class of MD-groups. The…

The Weyl group of a crystallographic root system has a nonlinear action on the compact torus. The orbit space of this action is a compact basic semi-algebraic set. We present a polynomial description of this set for the Weyl groups of type…

We use the theory of Clifford algebras and Vahlen groups to study Weyl groups of hyperbolic Kac-Moody algebras T_n^{++}, obtained by a process of double extension from a Cartan matrix of finite type T_n, whose corresponding generalized…

This paper is a continuation of arXiv:1201.1102. We investigate the orbit closures for the class of representations of simple algebraic groups associated to various gradings on the simple Lie algebra of type $E_7$. The methods for…

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras…

We suggest new realizations of quantum groups corresponding to complex simple Lie algebras, and of affine quantum groups. These new realizations are labeled by Coxeter elements of the corresponding Weyl group and have the following key…

Let C be the centralizer in a finite Weyl group of an elementary abelian 2-subgroup. We show that every complex representation of C can be realized over the field of rational numbers. The same holds for a Sylow 2-subgroup of C.

To classify the classical field theories with W-symmetry one has to classify the symplectic leaves of the corresponding W-algebra, which are the intersection of the defining constraint and the coadjoint orbit of the affine Lie algebra if…

We evaluate partition functions of matrix models which are given by topologically twisted and dimensionally reduced actions of d=4 N=1 super Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1) and USp(2N). The…

We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of…

We show that except in several cases conjugacy classes of classical Weyl groups $W(B_n)$ and $W(D_n)$ are of type {\rm D}. We prove that except in three cases Nichols algebras of irreducible Yetter-Drinfeld ({\rm YD} in short )modules over…