Related papers: The Sugawara generators at arbitrary level

Given a pair of smooth transversally intersecting manifolds in some ambient manifold, we construct an operator algebra generated by pseudodifferential operators and the (co)boundary operators associated with the submanifolds. We show that…

In this note we construct a series of singular vectors in universal affine vertex operator algebras associated to $D_{\ell}^{(1)}$ of levels $n-\ell+1$, for $n \in \Z_{>0}$. For $n=1$, we study the representation theory of the quotient…

Let G=U(p,q) and K=U(p)xU(q). In arXiv:0801.1530, the authors construct a functor from the category of Harish-Chandra modules for the pair (G,K) to the category of representations of the degenerate affine Hecke algebra of type B_n. In this…

We construct a vertex representation for the quantum toroidal algebra through the quantum general linear algebra. Using a new realization of the quantum general linear algebra we construct vertex operators for root vectors on the basic…

Let O_d be the Cuntz algebra on generators S_1,...,S_d, 2 \leq d < \infty, and let D_d \subset O_d be the abelian subalgebra generated by monomials S_\alpha S_\alpha^* =S_{\alpha_{1}}...S_{\alpha_{k}}S_{\alpha_{k}}^*...S_{\alpha_{1}}^*…

We develop a novel combinatorial perspective on the higher Auslander algebras of type $\mathbb{A}$, a family of algebras arising in the context of Iyama's higher Auslander-Reiten theory. This approach reveals interesting simplicial…

In this paper, we construct finite dimensional irreducible representations for two different versions of \Z2 graded $osp(1|2)$ algebra based on eight- and ten-generators. We find that there are two different second-order Casimir operators…

In the paper, we introduce and calculate difference Fourier transforms on representations of the double affine Hecke algebras in polynomilas, polynomials multiplied by the Gaussian, and various spaces of delta-functions including…

This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic surface. The crucial observation is that the algebra…

We provide a new representation of a refinable shift invariant space with a compactly supported generator, in terms of functions with a special property of homogeneity. In particular these functions include all the homogeneous polynomials…

We study the $\varphi$-Verma modules of the Heisenberg subalgebra $\mathcal{H}_m$ of the universal central extension of $\mathfrak{sl}_2 \otimes A_m$, where $A_m$ is the coordinate ring of the superelliptic curve $u^m = P(t)$, and ask how…

Consider a formally self-adjoint first order linear differential operator acting on pairs (2-columns) of complex-valued scalar fields over a 4-manifold without boundary. We examine the geometric content of such an operator and show that it…

We give a bosonization of the quantum affine superalgebra $U_q(\widehat{sl}(N|1))$ for an arbitrary level $k \in {\bf C}$. The bosonization of level $k \in {\bf C}$ is completely different from those of level $k=1$. From this bosonization,…

The perennial formalism is applied to the real, massive Klein-Gordon field on a globally-hyperbolic background space-time with compact Cauchy hypersurfaces. The parametrized form of this system is taken over from the accompanying paper. Two…

This paper presents a comprehensive study of H-Toeplitz operators on the Fock space, a class of operators that synthesizes structural elements of both Toeplitz and Hankel operators. We derive explicit matrix representations for these…

We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the…

In this paper, we construct a representation of loop group and derive the formula of the corresponding representation of the affine Kac-Moody algebra with level 1. And we also provide a concrete realization of Whittaker functionals in the…

In this paper, we study the $U(1)^2$ Kac--Moody algebra and generalize the standard Sugawara construction of the Virasoro algebra to an infinite family of new realizations. In this case, in addition to the standard invariant tensor…

In [14] we introduced a new class of algebras, which we named \textit{quantum generalized Heisenberg algebras} and which depend on a parameter $q$ and two polynomials $f,g$. We have shown that this class includes all generalized Heisenberg…

We compute generators and relations for a certain $2$-adic Hecke algebra of level $8$ associated with the double cover of $\mathrm{SL}_2$ and a $2$-adic Hecke algebra of level $4$ associated with $\mathrm{PGL}_2$. We show that these two…