Zobrazeno 1 - 10
of 121
pro vyhledávání: '"Saponov, P. A."'
Quantum differential operators on Reflection Equation Algebras, corresponding to Hecke symmetries R were introduced in previous publications. In the present paper we are mainly interested in quantum analogs of the Laplace and Casimir operators, which
Externí odkaz:
http://arxiv.org/abs/2412.13373
Autor:
Gurevich, Dimitry, Saponov, Pavel
We consider the so-called generalized Harish-Chandra morphism, taking the center of the enveloping algebra U(gl(N)) to the commutative algebra generated by eigenvalues of the generating matrix of this algebra, and generalize this construction to Refl
Externí odkaz:
http://arxiv.org/abs/2411.01303
Autor:
Gurevich, Dimitry, Saponov, Pavel
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of $A_m$ type, in particular, analogs of the partial derivatives and de Rham complex were defined. Also, we introduced the notion of qu
Externí odkaz:
http://arxiv.org/abs/2403.01819
Autor:
Gurevich, Dimitry, Saponov, Pavel
We establish a q-version of the Schur-Weyl duality, in which the role of the symmetric group is played by the Hecke algebra and the role of the enveloping algebra U(gl(N)) is played by the Reflection Equation algebra, associated with any skew-inverti
Externí odkaz:
http://arxiv.org/abs/2307.06677
In this note we are dealing with a particular class of quadratic algebras -- the so-called quantum matrix algebras. The well-known examples are the algebras of quantized functions on classical Lie groups (the RTT algebras). We consider the problem of
Externí odkaz:
http://arxiv.org/abs/2303.10749
Autor:
Gurevich, Dimitry, Saponov, Pavel
Publikováno v:
Journal of Geometry and Physics, vol. 171 (2022) 104396
We introduce analogs of creation and annihilation operators, related to involutive and Hecke symmetries R, and perform bosonic and fermionic realization of the modified Reflection Equation algebras in terms of the so-called Quantum Doubles of Fock ty
Externí odkaz:
http://arxiv.org/abs/2212.12699
Autor:
Gurevich, Dimitry, Saponov, Pavel
By treating generators of the reflection equation algebra corresponding to a Hecke symmetry as quantum analogs of vector fields, we exhibit the corresponding Leibniz rule via the so-called quantum doubles. The role of the function algebra in such a d
Externí odkaz:
http://arxiv.org/abs/2211.14376
Autor:
Dimitry Gurevich, Pavel Saponov
Publikováno v:
Partial Differential Equations in Applied Mathematics, Vol 11, Iss , Pp 100781- (2024)
In our previous publications we have developed some elements of Noncommutative calculus on the enveloping algebras of Am type, in particular, analogs of the partial derivatives and de Rham complex were defined. Also, we introduced the notion of quant
Externí odkaz:
https://doaj.org/article/797ac2acabd04c3c815cedd53f61f0f3
Publikováno v:
Journal of Geometry and Physics, 179 (2022) 104606
By using the notion of a quantum double we introduce analogs of partial derivatives on a Reflection Equation algebra, associated with a Hecke symmetry of GL(N) type. We construct the matrix L=MD, where M is the generating matrix of the Reflection Equ
Externí odkaz:
http://arxiv.org/abs/2207.02034
In this paper we are dealing with the Reflection Equation algebra ${\cal M}(R)$, associated with a $GL_N$ type Hecke symmetry $R$. In this algebra we define the $q$-analogs of the partial derivatives $\partial_j^i$ in generators $m_i^j$ of ${\cal M}(
Externí odkaz:
http://arxiv.org/abs/2110.04354