# Classical Isomorphisms for Quantum Groups

@article{Jain1992ClassicalIF, title={Classical Isomorphisms for Quantum Groups}, author={Vidyut Jain and O. Ogievetsky}, journal={arXiv: High Energy Physics - Theory}, year={1992} }

The expressions for the $\hat{R}$--matrices for the quantum groups SO$_{q^2}$(5) and SO$_q$(6) in terms of the $\hat{R}$--matrices for Sp$_q$(2) and SL$_q$(4) are found, and the local isomorphisms of the corresponding quantum groups are established.

#### 9 Citations

SUq(2) covariant
$$\hat R$$
-matrices for reducible representations

- Mathematics
- 1994

AbstractWe consider SUq(2) covariant
$$\hat R$$
-matrices for the reducible3 ⊕1 representation. There are three solutions to the Yang-Baxter equation. They coincide with the previously known
$$\hat… Expand

Quantum deformations of singletons and of free zero-mass fields

- Mathematics
- 1993

We consider quantum deformations of the real symplectic (or anti-De Sitter) algebra sp(4), ℝ ≅ spin(3, 2) and of its singleton and (4-dimensional) zero-mass representations. For q a root of −1, these… Expand

Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them

- Mathematics
- 2005

For families of orthogonal and symplectic types quantum matrix (QM-) algebras, we derive corresponding versions of the Cayley-Hamilton theorem. For a wider family of Birman-Murakami-Wenzl type… Expand

q-deformed conformal and Poincaré algebras on quantum 4-spinors

- Physics
- 1993

We investigate quantum deformation of conformal algebras by constructing the quantum space forslq(4). The differential calculus on the quantum space and the action of the quantum generators are… Expand

Quantum deformedsu(m/n) algebra and superconformal algebra on quantum superspace

- Physics
- 1993

We study a deformedsu(m/n) algebra on a quantum superspace. Some interesting aspects of the deformed algebra are shown. As an application of the deformed algebra we construct a deformed… Expand

Braidings of Tensor Spaces

- Mathematics
- 2012

Let V be a braided vector space, i.e., a vector space together with a solution $${\hat{R}\in {{End}}(V\otimes V)}$$ of the Yang–Baxter equation. Denote $${T(V):=\bigoplus_k V^{\otimes k}}$$ . We… Expand

Jucys--Murphy elements and representations of cyclotomic Hecke algebras

- Mathematics
- 2012

An inductive approach to the representation theory of cyclotomic Hecke algebras, inspired by Okounkov and Vershik, is developed. We study the common spectrum of the Jucys-Murphy elements using… Expand

Algèbres de Hecke cyclotomiques : représentations, fusion et limite classique.

- Mathematics
- 2012

Une approche inductive est developpee pour la theorie des representations de la chaine des algebres de Hecke cyclotomiques de type G(m,1,n). Cette approche repose sur l'etude du spectre d'une famille… Expand

Cayley–Hamilton theorem for symplectic quantum matrix algebras

- Mathematics, Physics
- Journal of Geometry and Physics
- 2021

Abstract We establish the analogue of the Cayley–Hamilton theorem for the quantum matrix algebras of the symplectic type. We construct the algebra in which the quantum characteristic polynomial… Expand

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Publisher Summary
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