Related papers: Drinfeld basis for string-inspired Baxter operator…
Baxter operators are constructed for quantum spin chains with deformed $s\ell_2$ symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier…
Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit…
We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\widehat{\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and…
We solve the following problem: to describe in geometric terms all differential operators of the second order with a given principal symbol. Initially the operators act on scalar functions. Operator pencils acting on densities of arbitrary…
Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a…
We introduce an analog of the Maxwell operator on a q-Minkowski space algebra (treated as a particular case of the so-called Reflection Equation Algebra) and on certain of its quotients. We treat the space of "quantum differential forms" as…
We give the construction of twisted quantum Lax equations associated with quantum groups. We solve these equations using factorization properties of the corresponding quantum groups. Our construction generalizes in many respects the…
The design and implementation of large sets of spatially-extended, gauge-invariant operators for use in determining the spectrum of baryons in lattice QCD computations are described. Group-theoretical projections onto the irreducible…
This paper addresses the question of how categorical symmetries act on extended operators in quantum field theory. Building on recent results in two dimensions, we introduce higher tube categories and algebras associated to higher fusion…
In this paper we continue to study Belavin-Drinfeld cohomology introduced in arXiv:1303.4046 [math.QA] and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra. Here we compute…
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $1/\sin^2(x)$ on the finite interval $(0,\pi)$, we now take a closer look at the underlying Bessel-type operators with more…
We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy…
We use variations on Lax type operators to find explicit formulas for certain elements of finite $W$-algebras. These give a complete set of generators for all finite $W$-algebras of types B,C,D for which the Dynkin grading is even.
The gauge compensation fields induced by the differential operators of the Stueckelberg-Schr\"odinger equation are discussed, as well as the relation between these fields and the standard Maxwell fields. An action is constructed and the…
Some relations between different objects associated with quantum affine algebras are reviewed. It is shown that the Frenkel-Jing bosonization of a new realization of quantum affine algebra $\Uqa$ as well as bosonization of $L$-operators for…
Possible generalizations of quantum theory permitting to describe in a unique way the development of the quantum system and the measurement process are discussed. The approach to the problem based on the Lindblad's equation for the…
We present some formulae for the Drazin inverse of difference and product of idempotents in a ring. A number of results of bounded linear operators in Banach spaces are extended to the ring case.
In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…
Quantum Drinfeld orbifold algebras are the generalizations of Drinfeld orbifold algebras, which are obtained by replacing polynomial rings by quantum polynomial rings. Shepler and Witherspoon in their paper, give necessary and sufficient…