相关论文: $gl_{n+1}$ algebra of Matrix Differential Operator…
We give a complete classification of conformally covariant differential operators between the spaces of differential $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$ by analyzing the restriction of…
The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of…
We show that the Gaudin Hamiltonians H_1,...,H_n generate the Bethe algebra of the n-fold tensor power of the vector representation of gl_N. Surprisingly the formula for the generators of the Bethe algebra in terms of the Gaudin…
Formulas for the solutions of initial value problems for ordinary differential equations with singular $\delta^{(n)}$-like driving terms are derived in the framework of an algebra of generalized functions (of Colombeau type) over a field of…
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…
We consider generalizations of Dunkl's differential-difference operators associated with groups generated by reflections. The commutativity condition is equivalent to certain functional equations. These equations are solved in many cases.…
The algebra of invariants of several 3 x 3 matrices under the action of the orthogonal group by simultaneous conjugation is considered over a field of characteristic different from two. The maximal degree of elements of minimal system of…
We construct a class of representations of the quadratic $R$-matrix algebra given by the reflection equation with the spectral parameter, $$ R{\,}(u-v)\,T^{(1)}(u)\,R{\,}(u+v)\,T^{(2)}(v)= T^{(2)}(v)\,R{\,}(u+v)\,T^{(1)}(u)\,R{\,}(u-v), $$…
We develop a representation theory approach to the study of generalized hypergeometric functions of Gelfand, Kapranov and Zelevisnky (GKZ). We show that the GKZ hypergeometric functions may be identified with matrix elements of…
For any orthogonal polynomials system on real line we construct an appropriate oscillator algebra such that the polynomials make up the eigenfunctions system of the oscillator hamiltonian. The general scheme is divided into two types: a…
We first establish some general results connecting real and complex Lie algebras of first-order differential operators. These are applied to completely classify all finite-dimensional real Lie algebras of first-order differential operators…
A method to construct in explicit form the generators of the simple roots of an arbitrary finite-dimensional representation of a quantum or standard semisimple algebra is found. The method is based on general results from the global theory…
The space of smooth sections of an equivariant line bundle over the real projective space $\mathbb{R}{\rm P}^n$ forms a natural representation of the group ${\rm GL}(n+1,\mathbb{R})$. We explicitly construct and classify all intertwining…
We introduce a construction of the differential calculus on the quantum supergroup GL$_{p,q}(1| 1)$. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum…
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…
We define quantum matrix groups GL(3) by their coaction on appropriate quantum planes and the requirement that the Poincare series coincides with the classical one. It is shown that this implies the existence of a Yang-Baxter operator.…
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential…
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
In recent years, digraph induced generators of quantum dynamical semigroups have been introduced and studied, particularly in the context of unique relaxation and invariance. In this article we define the class of pair block diagonal…