ترغب بنشر مسار تعليمي؟ اضغط هنا

Simple bounded highest weight modules of basic classical Lie superalgebras

242   0   0.0 ( 0 )
 نشر من قبل Dimitar Grantcharov
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of $mathfrak g$.



قيم البحث

اقرأ أيضاً

In this paper, a family of non-weight modules over Lie superalgebras $S(q)$ of Block type are studied. Free $U(eta)$-modules of rank $1$ over Ramond-Block algebras and free $U(mathfrak{h})$-modules of rank $2$ over Neveu-Schwarz-Block algebras are co nstructed and classified. Moreover, the sufficient and necessary conditions for such modules to be simple are presented, and their isomorphism classes are also determined. The results cover some existing results.
We prove that the tensor product of a simple and a finite dimensional $mathfrak{sl}_n$-module has finite type socle. This is applied to reduce classification of simple $mathfrak{q}(n)$-supermodules to that of simple $mathfrak{sl}_n$-modules. Rough st ructure of simple $mathfrak{q}(n)$-supermodules, considered as $mathfrak{sl}_n$-modules, is described in terms of the combinatorics of category $mathcal{O}$.
In this paper the authors introduce a class of parabolic subalgebras for classical simple Lie superalgebras associated to the detecting subalgebras introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to have good cohomological properties governed by the Bott-Borel-Weil theorem involving the zero component of the Lie superalgebra in conjunction with the odd roots. These results are later used to verify an open conjecture given by Boe, Kujawa and Nakano pertaining to the equality of various support varieties.
In 2006, Gao and Zeng cite{GZ} gave the free field realizations of highest weight modules over a class of extended affine Lie algebras. In the present paper, applying the technique of localization to those free field realizations, we construct a clas s of new weight modules over the extended affine Lie algebras. We give necessary and sufficient conditions for these modules to be irreducible. In this way, we construct free field realizations for a class of simple weight modules with infinite weight multiplicities over the extended affine Lie algebras.
Let ${mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${mathcal W}_n$-modules $M$ with finite weight multiplicities. We prove that every such nontrivial module $M$ is either a tensor module or the unique simple submodule in a tensor module associated with the de Rham complex on $mathbb C^n$.
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