ﻻ يوجد ملخص باللغة العربية
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 $U_{-q^2}mathfrak{so}_n$. For $N$ even, an analogous statement also holds for $S=S_+oplus S_-$ the direct sum of the irreducible spinor representations of $U_qmathfrak{so}_N$, with the commutant given by $U_{-q}mathfrak{o}_n$, a $mathbb{Z}/2$-extension of $U_{-q}mathfrak{so}_n$. Similar statements also hold for fusion tensor categories with $q$ a root of unity.
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
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
We study representations of the non-standard quantum deformation $U_qso_n$ of $Uso_n$ via a Verma module approach. This is used to recover the classification of finite-dimensional modules for $q$ not a root of unity, given by classical and non-classi
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
We derive a formula for the trace of the antipode on endomorphism algebras of simple self-dual modules of nilpotent liftings of quantum planes. We show that the trace is equal to the quantum dimension of the module up to a nonzero scalar depending on the simple module.