相关论文: Commuting difference operators arising from the el…

We study a pair of commuting difference operators arising from the elliptic solution of the dynamical Yang-Baxter equation of type C_2. The operators act on the space of meromorphic functions on the weight space of sp(4,C). We show that…

We study a family of mutually commutative difference operators associated with the affine root systems. These operators act on the space of meromorphic functions on the Cartan subalgebra of the affine Lie algebra. We show that the space…

For Belavin's elliptic quantum R-matrix, we construct an L-operator as a set of difference operators acting on functions on the type A weight space. According to the fundamental relation $RLL=LLR$, the trace of the L-operator gives a…

We demonstrate a method of associating the principal symbol at a $K$-point with a linear differential operator acting between modules over a commutative algebra, and we use it to define the ellipticity of a linear differential operator in a…

We consider quantum mechanics on the noncommutative spaces characterized by the commutation relations $$ [x_a, x_b] \ =\ i\theta f_{abc} x_c\,, $$ where $f_{abc}$ are the structure constants of a Lie algebra. We note that this problem can…

In this paper we study commuting difference operators containing a shift operator with only positive degrees. We construct examples of such operators in the case of hyperelliptic spectral curves.

We consider one-point commuting difference operators of rank one. The coefficients of these operators depend on a functional parameter, shift operators being included only with positive degrees. We study these operators in the case of…

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…

We consider the standard hypergeometric differential operator $D$ regarded as an operator on the complex plane $C$ and the complex conjugate operator $\overline D$. These operators formally commute and are formally adjoint one to another…

In this article, we investigate differential operators on the Siegel-Jacobi space that are invariant under the natural action of the Jacobi group. These invariant differential operators play an important role in the arithmetic theory of…

In this paper we continue the study of the superconformal index of four-dimensional $\mathcal{N}=2$ theories of class $\mathcal{S}$ in the presence of surface defects. Our main result is the construction of an algebra of difference…

We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the…

We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show…

We study the quantum analogs of tops on Lie algebras $so(4)$ and $e(3)$ represented by differential operators.

For quantum integrable models with elliptic R-matrix, we construct the Baxter Q-operator in infinite-dimensional representations of the algebra of observables.

In this paper we find new self-adjoint commuting operators of rank 2 with rational coefficients and prove that any elliptic and hyperelliptic curves of genus 2 are spectral curves of commuting operators with rational coefficients. Also the…

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…

We introduce twists by Cartan elements of conformal blocks on a curve X, corresponding to a Lie algebra g. We show that these twists define holomorphic functions, with theta-like behaviour, on a product of copies of its Jacobian J(X)^r. We…

We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show it's commutation with certain Hecke operators and use it to construct a lift of elliptic cusp forms to Hermitian Jacobi cusp forms.…

In this paper we study self-adjoint commuting ordinary differential operators with polynomial coefficients. These operators define commutative subalgebras of the first Weyl algebra. We find new examples of commuting operators of rank 2.