相关论文: Explicit construction of companion bases
We give a model-independent construction of directed univalent cocartesian fibrations of $(\infty,1)$-categories, and prove a straightening equivalence against such fibrations. The key step is showing that cocartesian fibrations descend…
We propose a new simple model for DNA denaturation bases on the pendulum model of Englander\cite{A1} and the microscopic model of Peyrard {\it et al.},\cite{A3} so called "combined model". The main parameters of our model are: the coupling…
In this note, we give very simple constructions of unique neighbor expander graphs starting from spectral or combinatorial expander graphs of mild expansion. These constructions and their analysis are simple variants of the constructions of…
We suggest a (conjectural) construction of a basis in the plus part of the affine Lie algebra of type ADE indexed by irreducible components of certain quiver varieties. This construction is closely related to a string-theoretic construction…
We use the language of quivers to formulate a mathematical framework for phylogenetics.
In pointed braided fusion categories knowing the self-symmetry braiding of simples is theoretically enough to reconstruct the associator and braiding on the entire category (up to twisting by a braided monoidal auto-equivalence). We address…
We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp.…
We compute the minimal model for Ginzburg algebras associated to acyclic quivers $Q$. In particular, we prove that there is a natural grading on the Ginzburg algebra making it formal and quasi-isomorphic to the preprojective algebra in…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
Following a question of Vinberg, a general method to construct monomial bases for finite-dimensional irreducible representations of a reductive Lie algebra was developed in a series of papers by Feigin, Fourier, and Littelmann. Relying on…
We show that for two quivers without oriented cycles related by a BGP reflection, the posets of their cluster tilting objects are related by a simple combinatorial construction, which we call a flip-flop. We deduce that the posets of…
We describe a new way to construct finite geometric objects. For every k we obtain a symmetric configuration E(k-1) with k points on a line. In particular, we have a constructive existence proof for such configurations. The method is very…
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are…
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
A simple quark-diquark model of baryons with direct and exchange interactions is constructed. Spectrum and form factors are calculated and compared with experimental data. Advantages and disadvantages of the model are discussed.
We study $3d$ $\mathcal{N}=4$ quiver gauge theories with gauge nodes forming a $D_n$ Dynkin diagram. The class of good $D_n$ Dynkin quivers is completely characterised and the moduli space singularity structure fully determined for all such…
Starting from a locally gentle bound quiver, we define on the one hand a simplicial complex, called the non-kissing complex. On the other hand, we construct a punctured, marked, oriented surface with boundary, endowed with a pair of dual…
We provide several constructions of special unextendible entangled bases with fixed Schmidt number $k$ (SUEB$k$) in $\mathbb{C}^{d}\otimes \mathbb{C}^{d'}$ for $2\leq k\leq d\leq d'$. We generalize the space decomposition method in Guo…
In the representation theory of simple Lie algebras, we consider the problem of constructing a monomial basis in an arbitrary irreducible finite-dimensional highest weight module. We construct a PBW-type basis in every finite-dimensional…