Related papers: LLT polynomials in the Schiffmann algebra
We study Toeplitz-type operators with respect to specific wavelets whose Fourier transforms are related to Laguerre polynomials. On the one hand, this choice of wavelets underlines the fact that these operators acting on wavelet subspaces…
We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the…
We construct a new family of graded representations $\widetilde{W}_{\lambda}$ for the positive elliptic Hall algebra $\mathcal{E}^{+}$ indexed by Young diagrams $\lambda$ which generalize the standard $\mathcal{E}^{+}$ action on symmetric…
We present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers Getzler's original functor but allows us to prove the…
We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This…
We show that a ratio of Schur polynomials $s_{\lambda}/s_{\rho}$ associated to partitions $\lambda$ and $\rho$ such that $\lambda\subsetneq\rho$ has a negative partial derivative at any point where all variables are positive. This is…
We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain $D$ of ${\mathbb R}^n$ for a second order parameter-dependent elliptic differential operator $A (x,\partial, \lambda)$ with complex-valued essentially…
We construct a new family of graded representations $\widetilde{W}_{\lambda}$ indexed by Young diagrams $\lambda$ for the positive elliptic Hall algebra $\mathcal{E}^{+}$ which generalizes the standard $\mathcal{E}^{+}$ action on symmetric…
Let $L$ be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces $L^{p}(R^{n};X)$ of $X$-valued functions on $R^n$. We characterize Kato's square root estimates $\|\sqrt{L}u\|_{p} \eqsim \|\nabla…
We consider here a new operator, called ``super nabla'', which is shown to be generic among operators for which the modified Macdonald polynomials are joint eigenfunctions. All previously known Macdonald eigenoperators can readily be…
We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Moreover,…
Weighted Rota-Baxter operators on associative algebras are closely related to modified Yang-Baxter equations, splitting of algebras, weighted infinitesimal bialgebras, and play an important role in mathematical physics. For any $\lambda \in…
Let $\lambda =\left( \lambda_{1},\lambda_{2},...,\lambda_{r}\right) $ be an integer partition, and $\left[p_{\lambda }\right] $ the $q$-analog of the symmetric power function $%p_{\lambda }$. This $q$-analogue has been defined as a special…
The Bernstein operator $\mathbf{B}_n$ acts on a Schur function $S_\lambda$ by appending a part to the index, i.e., $\mathbf{B}_n S_\lambda=S_{(n,\lambda)}$. This provides a method of constructing the vertex operator representation of Schur…
We study the rational Cherednik algebra attached to the complex reflection group $G(r,1,2)$. Each irreducible representation $S^\lambda$ of $G(r,1,2)$ corresponds to a standard module $\Delta(\lambda)$ for the rational Cherednik algebra. We…
This is the final part of a series of papers where we study perturbations of divergence form second order elliptic operators $-\operatorname{div} A \nabla$ by first and zero order terms, whose complex coefficients lie in critical spaces,…
A new analytic model for left-invertible operators, which extends both Shimorin's analytic model for left-invertible and analytic operators and Gellar's model for bilateral weighted shift is introduced and investigated. We show that a…
We extend the $\lambda$-theory of operator spaces given by Defant and Wiesner (2014), that generalizes the notion of the projective, Haagerup and Schur tensor norm for operator spaces to matrix ordered spaces and Banach $*$-algebras. Given…
We introduce the logics GLP(\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\omega) where \Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength. We shall…
When is the collection of $\mathsf S$-Toeplitz operators with respect to a tuple of commuting bounded operators $\mathsf S= (S_1, S_2, \ldots , S_{d-1}, P)$, which has the symmetrized polydisc as a spectral set, non-trivial? The answer is…