Related papers: Ad-nilpotent Ideals and Equivalence Relations

Let $G_{\mathbb R}$ be the set of real points of a complex linear reductive group and $\hat G_\lambda$ its classes of irreducible admissible representations with infinitesimal integral regular character $\lambda$. In this case each cell of…

The intersection cohomologies of closures of nilpotent orbits of linear (respectively, cyclic) quivers are known to be described by Kazhdan-Lusztig polynomials for the symmetric group (respectively, the affine symmetric group). We explain…

We prove that the Khovanov-Lauda-Rouquier algebras $R_\al$ of type $A_\infty$ are (graded) affine cellular in the sense of Koenig and Xi. In fact, we establish a stronger property, namely that the affine cell ideals in $R_\al$ are generated…

We propose the study and description of the structure of complex Lie algebras with nilradical a nilpotent Lie algebra of type 2 by using sl2(C)-representation theory. Our results will be applied to review the classification given in [1] (J.…

Given a simply connected solvable Lie group $G$, there always exists NIL-affine action $\rho: G \to \operatorname{Aff}(H)$ on a nilpotent Lie group $H$ such that $G$ acts simply transitively. The question whether this is always possible for…

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

We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with…

We conjecture that the "nilpotent points" of Calogero-Moser space for reflection groups are parametrised naturally by the two-sided cells of the group with unequal parameters. The nilpotent points correspond to blocks of restricted…

We study the crystal of quantum nilpotent subalgebra of $U_q(D_n)$ associated to a maximal Levi subalgebra of type $A_{n-1}$. We show that it has an affine crystal structure of type $D_n^{(1)}$ isomorphic to a limit of perfect…

A Lie algebra L is known to be nilpotent if it admits a grading by (Zp, +) with support X not containing 0. It is also known that the class of L can be bounded by some explicit function of |X|. We generalise this and other classical results…

We classify the finite dimensional irreducible representations with integral central character of finite $W$-algebras $U(\mathfrak g,e)$ associated to standard Levi nilpotent orbits in classical Lie algebras of types B and C. This…

We study some applications of solvable Lie algebras in type IIA, type IIB and M theories. RR and NS generators find a natural geometric interpretation in this framework. Special emphasis is given to the counting of the abelian nilpotent…

We prove a weak version of Lusztig's conjecture on explicit description of the asymptotic Hecke algebras (both finite and affine), and explain its relation to Lusztig's classification of character sheaves.

We prove that generic higher Deligne-Lusztig representations over truncated formal power series are non-nilpotent, when the parameters are non-trivial on the biggest reduction kernel of the centre; we also establish a relation between the…

We introduce a concept of approximately invertible elements in non-unital normed algebras which is, on one side, a natural generalization of invertibility when having approximate identities at hand, and, on the other side, it is a direct…

A conformal Lie group is a conformal manifold $(M,c)$ such that $M$ has a Lie group structure and $c$ is the conformal structure defined by a left-invariant metric $g$ on $M$. We study Weyl-Einstein structures on conformal solvable Lie…

Let D(e) denote the weighted Dynkin diagram of a nilpotent element $e$ in complex simple Lie algebra $\g$. We say that D(e) is divisible if D(e)/2 is again a weighted Dynkin diagram. (That is, a necessary condition for divisibility is that…

The notion of defining relations is well-defined for any nilpotent Lie algebra. Therefore a conventional way to present a simple Lie algebra G is by splitting it into the direct sum of a commutative Cartan subalgebra and two maximal…

We construct a family of potentially quasi-lisse (non-rational) vertex algebras, denoted by $\mathcal{C}_p$, $p \geq 2$, which are closely related to the vertex algebra of chiral differential operators on $SL(2)$ at level $-2+\frac{1}{p}$.…

Several very interesting results connecting the theory of abelian ideals of Borel subalgebras, some ideas of D. Peterson relating the previous theory to the combinatorics of affine Weyl groups, and the theory of discrete series are stated…