相关论文: Decomposition of D-modules over a hyperplane arran…
We study the Weyl groups of hyperbolic Kac-Moody algebras of `over-extended' type and ranks 3, 4, 6 and 10, which are intimately linked with the four normed division algebras K=R,C,H,O, respectively. A crucial role is played by integral…
A sequence is difference algebraic (or D-algebraic) if finitely many shifts of its general term satisfy a polynomial relationship; that is, they are the coordinates of a generic point on an affine hypersurface. The corresponding equations…
This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…
Let $G$ be an almost simple simply connected group over complex numbers. For a positive element $\alpha$ of the coroot lattice of $G$ let $Z^\alpha$ denote the space of based maps from the projective line to the flag variety of $G$ of…
Let $A$ be a commutative, associative algebra with unity over $\mathbb{C}$. Using the definition of global Weyl modules for the map superalgebras given by Calixto, Lemay, and Savage we explicitly describe the structure of certain quotients…
We compute the finite-dimensional Nichols algebras over the sum of two simple Yetter-Drinfeld modules V and W over non-abelian quotients of a certain central extension of the dihedral group of eight elements or SL(2,3), and such that the…
We investigate the permutation modules associated to the set of $k$-dimensional faces of the hyperoctahedron in dimension $n$, denoted $H^{n}.$ For any $k\leq n$ such a module can be defined over an arbitrary field $F$, it is called a face…
A line pattern in a free group $F$ is defined by a malnormal collection of cyclic subgroups. Otal defined a decomposition space $\mathcal{D}$ associated to a line pattern. We provide an algorithm that computes a presentation for the…
The purpose of this article is to investigate relations between W-superalgebras and integrable super-Hamiltonian systems. To this end, we introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie superalgebra $g$ and…
We study the algebra of Weyl modules in types $A$ and $C$ using the methods of arcs over toric degenerations and functional realization of dual space. We compute the generators and relations of this algebra and construct its basis.
The Euler-Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler-Koszul homology with D-module direct images from the torus to the base space through orbits…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
We study the irregularity of hypergeometric D-modules $\mathcal{M}_A (\beta )$ via the explicit construction of Gevrey series solutions along coordinate subspaces in $X =\mathbb{C}^n$. As a consequence, we prove that along coordinate…
We use the theory of hyperplane arrangements to construct natural bases for the homology of partition lattices of types A, B and D. This extends and explains the "splitting basis" for the homology of the partition lattice given in [Wa96],…
Differentially-algebraic (D-algebraic) functions are solutions of polynomial equations in the function, its derivatives, and the independent variables. We revisit closure properties of these functions by providing constructive proofs. We…
We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex…
The symplectic blob algebra is a physically motivated quotient of the Hecke algebra $H(\tilde{C}_n)$ with a diagram calculus. We find the blocks for the symplectic blob algebra for all specialisations of its parameters over the complex…
In vertex algebra theory, fusion rules are described as the dimension of the vector space of intertwining operators between three irreducible modules. We describe fusion rules in the category of weight modules for the Weyl vertex algebra.…
We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic…