ﻻ يوجد ملخص باللغة العربية
We give a presentation of the centralizer algebras for tensor products of spinor representations of quantum groups via generators and relations. In the even-dimensional case, this can be described in terms of non-standard q-deformations of orthogonal Lie algebras; in the odd-dimensional case only a certain subalgebra will appear. In the classical case q = 1 the relations boil down to Lie algebra relations.
Let $S$ be the spinor representation of $U_qmathfrak{so}_N$, for $N$ odd and $q^2$ not a rooot of unity. We show that the commutant of its action on $S^{otimes n}$ is given by a representation of the nonstandard quantum group $U_{-q^2}mathfrak{so}_n$
We show that ${rm End}_{bf U}(V_lambdaotimes V^{otimes n})$ is generated by the affine braid group $AB_n$ where ${bf U}=U_qmathfrak g(G_2)$, $V$ is its 7-dimensional irreducible representation and $V_lambda$ is an arbitrary irreducible representation.
In this paper we introduce a trace-like invariant for the irreducible representations of a finite dimensional complex Hopf algebra H. We do so by considering the trace of the map induced by the antipode S on the endomorphisms End(V) of a self-dual mo
Quantum N-toroidal algebras are generalizations of quantum affine algebras and quantum toroidal algebras. In this paper we construct a level-one vertex representation of the quantum N-toroidal algebra for type C. In particular, we also obtain a level
In this paper, we give a criterion on the semisimplicity of quantized walled Brauer algebras $mathscr B_{r,s}$ and classify its simple modules over an arbitrary field $kappa$.