Related papers: Level one Weyl modules for toroidal Lie algebras
This paper is the study of finite-dimensional graded representations of current lie superalgebras $\mathfrak{sl}(1|2)[t]$. We define the notion of super POPs, a combinatorial tool to provide another parametrization of the basis of the local…
In this paper we classify the irreducible integrable modules for the twisted toroidal extended affine Lie algebras with center acting non-trivially.
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 first Weyl algebra over $k$, $A_1 = k \langle x, y\rangle/(xy-yx - 1)$ admits a natural $\mathbb{Z}$-grading by letting $\operatorname{deg} x = 1$ and $\operatorname{deg} y = -1$. Paul Smith showed that $\operatorname{gr}- A_1$ is…
Quantum N-toroidal algebras are generalizations of quantum affine algebras and quantum toroidal algebras. In this paper we construct a level-one vertex representation of the quantum N-toroidal algebra for type C. In particular, we also…
We derive a formula for the the modular class of a Lie algebroid with a regular twisted Poisson structure in terms of a canonical Lie algebroid representation of the image of the Poisson map. We use this formula to compute the modular…
This is the third in a sequence of four papers, where we prove the arithmetic Siegel--Weil formula in co-rank $1$ for Kudla--Rapoport special cycles on exotic smooth integral models of unitary Shimura varieties of arbitrarily large even…
We calculate the fusion rules among $\mathbb{Z}_2$-twisted modules $L_{\mathfrak{sl}_2}(\ell,0)$ at admissible levels. We derive a series MLDEs for normalized characters of ordinary twisted modules of quasi-lisse vertex algebras. Examples…
This paper introduces and studies a class of Weyl-type algebras \(A_{p,t,\cA} = \Weyl{e^{\pm x^{p} e^{t x}},\; e^{\cA x},\; x^{\cA}}\) constructed over exponential-polynomial rings, where \(\FF\) is a field of characteristic zero, \(\cA\)…
We show that the Fourier-Laplace transform of a regular holonomic module over the Weyl algebra of one variable, which generically underlies a variation of polarized Hodge structure, underlies itself an integrable variation of polarized…
Let $W_n^+$ be the Lie algebra of the Lie algebra of vector fields on $\C^n$. In this paper, we classify all simple bounded weight $W_n^+$ modules. Any such module is isomorphic to the simple quotient of a tensor module $F(P,M)=P\otimes M$…
The present paper deals with the representation theory of the reflection equation algebra, connected with a Hecke type R-matrix. Up to some reasonable additional conditions the R-matrix is arbitrary (not necessary originated from quantum…
We consider the standard modules of rectangular highest weights of affine Lie algebras in types $A_{2l-1}^{(2)}$ and $D_{l+1}^{(2)}$. By using vertex algebraic techniques we construct the combinatorial bases for standard modules and their…
We classify the derivations of degree-one generalized Weyl algebras over a univariate Laurent polynomial ring. In particular, our results cover the Weyl-Hayashi algebra, a quantization of the first Weyl algebra arising as a primitive factor…
Let A denote the ring of differential operators on the affine line with its two usual generators t and d/dt given degrees +1 and -1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups…
In this paper, we construct, investigate and, in some cases, classify several new classes of (simple) modules over the Takiff $\mathfrak{sl}_{2}$. More precisely, we first explicitly construct and classify, up to isomorphism, all modules…
We introduce a notion of a (V,T)-module over a vertex algebra V for an arbitrary positive integer T, which is a generalization of a twisted V-module. Under some conditions on V, we construct an associative algebra A^{T}_{m}(V) for…
In this paper we study the family of prime irreducible representations of quantum affine $\lie{sl}_{n+1}$ which arise from the work of D. Hernandez and B. Leclerc. These representations can also be described as follows: the highest weight…
A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…
An explicit vertex operator algebra construction is given of a class of irreducible modules for toroidal Lie algebras.