相关论文: A characterization of Dynkin elements

For a finite-dimensional representation V of a group G we introduce and study the notion of a Lie element in the group algebra k[G]. The set L(V) \subset k[G] of Lie elements is a Lie algebra and a G-module acting on the original…

One of the four well-known series of simple Lie algebras of Cartan type is the series of Lie algebras of Special type, which are divergence-free Lie algebras associated with polynomial algebras and the operators of taking partial…

Let $K$ be a local non-Archimedean field of positive characteristic and let $L$ be the degree-$n$ unramified extension of $K$. Via the local Langlands and Jacquet-Langlands correspondences, to each sufficiently generic multiplicative…

For every semi-simple Lie algebra one can construct the Drinfeld-Jimbo algebra U. This algebra is a deformation Hopf algebra defined by generators and relations. To study the representation theory of U, Drinfeld used the KZ-equations to…

This is a continuation of arXiv:0903.0398 [math.RT]. Let g be a simple Lie algebra. In this note, we provide simple formulae for the index of sl(2)-subalgebras in the classical Lie algebras and a new formula for the index of the principal…

Using the classification theorem due to Kac we prove that any finite dimensional simple Lie superalgebra over an algebraically closed field of characteristic 0 is generated by one element.

Let $\Q$ be the quiver of Dynkin type $\mathbb{A}_n$ with linear orientation and $A_{n}=k\Q$. In this paper, we give a complete classification of the silted algebras of type $A_{n}$ by using the geometric models of gentle algebras. We show…

Let L be a finite dimensional simple Lie algebra over an algebraically closed field of characteristic p>3. We prove in this paper that if all tori of maximal dimansion in the semisimple p-envelope of L are standard, the L is up to…

This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's…

Let "$\leq_L$" be the Kazhdan-Lusztig left cell preorder on the symmetric group $S_n$. Let $w\mapsto (P(w),Q(w))$ be the Robinson-Schensted-Knuth correspondence between $S_n$ and the set of standard tableaux with the same shapes. We prove…

Engel subalgebras of finite-dimensional n-Lie algebras are shown to have similar properties to those of Lie algebras. Using these, it is shown that an n-Lie algebra, all of whose maximal subalgebras are ideals, is nilpotent. A primitive…

Let L be a simple finite-dimensional Lie algebra of characteristic distinct from 2 and from 3. Suppose that L contains an extremal element that is not a sandwich, that is, an element x such that [x, [x, L]] is equal to the linear span of x…

Let $g$ be an affine Lie algebra with index set $I = \{0, 1, 2,..., n\}$ and $g^L$ be its Langlands dual. It is conjectured that for each $i \in I \setminus \{0\}$ the affine Lie algebra $g$ has a positive geometric crystal whose…

In this paper the authors provide a complete answer to Donkin's Tilting Module Conjecture for all rank $2$ semisimple algebraic groups and $\text{SL}_{4}(k)$ where $k$ is an algebraically closed field of characteristic $p>0$. In the…

We observe that on the level of derived categories, representations of the Lie algebra of a semisimple algebraic group over a field of characteristic $p> h$ (where $h$ is the Coxeter number), with a given (generalized) central character are…

Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on X with the structure of a restricted Lie algebra. We consider deformation quantization of line…

These notes are based on a course given at the EPFL in May 2005. It is concerned with the representation theory of Hecke algebras in the non-semisimple case. We explain the role that these algebras play in the modular representation theory…

Let $g$ be a simple Lie algebra and $Ab(g)$ the set of Abelian ideals of a Borel subalgebra of $g$. In this note, an interesting connection between $Ab(g)$ and the subsets of the Dynkin diagram of $g$ is discussed. We notice that the number…

Distinguished involutions in the affine Weyl groups, defined by G. Lusztig, play an essential role in the Kazhdan-Lusztig combinatorics of these groups. A distinguished involution is called canonical if it is the shortest element in its…

Let $L_{l}=L(\mathfrak{sl}_{2l+1},-l-\frac{1}{2})$ be the simple vertex operator algebra based on the affine Lie algebra $\widehat{\mathfrak{sl}}_{2l+1}$ at boundary admissible level $-l-\frac{1}{2}$. We consider a lift $\nu$ of the Dynkin…