ترغب بنشر مسار تعليمي؟ اضغط هنا

On centralizer algebras for spin representations

44   0   0.0 ( 0 )
 نشر من قبل Hans Wenzl
 تاريخ النشر 2011
  مجال البحث
والبحث باللغة English
 تأليف Hans Wenzl




اسأل ChatGPT حول البحث

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.

قيم البحث

اقرأ أيضاً

36 - Hans Wenzl 2020
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 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.
229 - Andrea Jedwab 2009
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 dule V. We also compute the values of this trace for the representations of two non-semisimple Hopf algebras: u_q(sl_2) and D(H_n(q)), the Drinfeld double of the Taft algebra.
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 -one module of the quantum toroidal algebra for type C as a special case.
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 $kappa$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا