Related papers: Canonical structure constants for simple Lie algeb…

We introduce a purely Lie algebraic formalization of the Feigin--Tipunin's geometric construction of logarithmic CFTs/VOAs. After reformulating the geometric representation theory of FT construction under this new setting, within this…

Commutative post-Lie algebra structures on Lie algebras, in short CPA structures, have been studied over fields of characteristic zero, in particular for real and complex numbers motivated by geometry. A perfect Lie algebra in…

All results concern characteristic 2. Two procedures that to every simple Lie algebra assign simple Lie superalgebras, most of the latter new, are offered. We prove that every simple finite-dimensional Lie superalgebra is obtained as the…

We compute lower bounds for Kazhdan constants of Chevalley groups over the integers, endowed with the standard Steinberg generators. For types other than $\mathtt{A}_{n}$, these are the first explicit asymptotically sharp such bounds. The…

We compute icanonical basis of the quasi-split rank one modified iquantum group, by obtaining explicit transition matrices among the icanonical basis, monomial basis, and standardized canonical basis; all these bases can be naturally…

We propose a construction of some canonical bases for quantum loop algebras of Kac-Moody algebras. We consider a smooth projective curve X, a group of automorphism G of X such that X/G=P^1, and we consider some Quot schemes of G-equivariant…

A formula for the structure constants of the multiplication of Schubert classes is obtained in arXiv:1909.05283. In this note, we prove analogous formulae for the Chern--Schwartz--MacPherson (CSM) classes and Segre--Schwartz--MacPherson…

For a finite dimensional simple complex Lie algebra $\mathfrak{g}$, Lie bialgebra structures on $\mathfrak{g}[[u]]$ and $\mathfrak{g}[u]$ were classified by Montaner, Stolin and Zelmanov. In our paper, we provide an explicit algorithm to…

The index of a finite-dimensional Lie algebra $g$ is the minimum of dimensions of stabilisers $g_\alpha$ of elements $\alpha\in g^*$. Let $g$ be a reductive Lie algebra and $z(x)$ a centraliser of a nilpotent element $x\in g$. Elashvili has…

For $\mathfrak{g}$ a simple Lie algebra and $G$ its adjoint group, the Chevalley map and work of Coxeter gives a concrete description of the algebra of $G$-invariant polynomials on $\mathfrak{g}$ in terms of traces over various…

Crystal basis theory for the queer Lie superalgebra was developed by Grantcharov et al. and it was shown that semistandard decomposition tableaux admit the structure of crystals for the queer Lie superalgebra or simply…

Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.

We obtain a formula for structure constants of certain variant form of Bott-Samelson classes for equivariant oriented cohomology of flag varieties. Specializing to singular cohomology/K-theory, we recover formulas of structure constants of…

For the BGG category of $\mathfrak{q}(n)$-modules of half-integer weights, a Kazhdan-Lusztig conjecture \`a la Brundan is formulated in terms of categorical canonical basis of the $n$th tensor power of the natural representation of the…

In this note we introduce the notion of $T^*-$extension $T^*{\mathfrak g}$ of a Lie superalgebra ${\mathfrak g}$, i.e. an extension of ${\mathfrak g}$ by its dual space ${\mathfrak g}^*$. The natural pairing induces on $T^*{\mathfrak g}$ an…

We study the algebraic constraints on the structure of nilpotent Lie algebra $\mathbb{g}$, which arise because of the presence of an integrable complex structure $J$. Particular attention is paid to non-abelian complex structures.…

We generalize the formula for the log canonical threshold(LCT) of plane curves over the complex numbers to arbitrary characteristics. Our proof relies purely on valuation theory, instead of on the theory of $D$-modules.

Lie algebras of dimension $n$ are defined by their structure constants , which can be seen as sets of $N = n^2 (n -- 1)/2$ scalars (if we take into account the skew-symmetry condition) to which the Jacobi identity imposes certain quadratic…

Let ${\mathcal B}_{\mathfrak{q}}$ be a finite-dimensional Nichols algebra of diagonal type with braiding matrix $\mathfrak{q}$, let $\mathcal{L}_{\mathfrak{q}}$ be the corresponding Lusztig algebra as in arXiv:1501.04518 and let…

We construct a nonuniform lattice and an infinite family of uniform lattices in the automorphism group of a hyperbolic building with all links a fixed finite building of rank 2 associated to a Chevalley group. We use complexes of groups and…