اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIrreducible Witt modules from Weyl modules and $mathfrak{gl}_{n}$-modules
179
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
For an irreducible module $P$ over the Weyl algebra $mathcal{K}_n^+$ (resp. $mathcal{K}_n$) and an irreducible module $M$ over the general liner Lie algebra $mathfrak{gl}_n$, using Shens monomorphism, we make $Potimes M$ into a module over the Witt algebra $W_n^+$ (resp. over $W_n$). We obtain the necessary and sufficient conditions for $Potimes M$ to be an irreducible module over $W_n^+$ (resp. $W_n$), and determine all submodules of $Potimes M$ when it is reducible. Thus we have constructed a large family of irreducible weight modules with many different weight supports and many irreducible non-weight modules over $W_n^+$ and $W_n$.
قيم البحث
اقرأ أيضاً
Let $n>1$ be an integer, $alphain{mathbb C}^n$, $bin{mathbb C}$, and $V$ a $mathfrak{gl}_n$-module. We define a class of weight modules $F^alpha_{b}(V)$ over $sl_{n+1}$ using the restriction of modules of tensor fields over the Lie algebra of vector
fields on $n$-dimensional torus. In this paper we consider the case $n=2$ and prove the irreducibility of such 5-parameter $mathfrak{sl}_{3}$-modules $F^alpha_{b}(V)$ generically. All such modules have infinite dimensional weight spaces and lie outside of the category of Gelfand-Tsetlin modules. Hence, this construction yields new families of irreducible $mathfrak{sl}_{3}$-modules.
Let $dge1$ be an integer, $W_d$ and $mathcal{K}_d$ be the Witt algebra and the weyl algebra over the Laurent polynomial algebra $A_d=mathbb{C} [x_1^{pm1}, x_2^{pm1}, ..., x_d^{pm1}]$, respectively. For any $mathfrak{gl}_d$-module $M$ and any admissib
le module $P$ over the extended Witt algebra $widetilde W_d$, we define a $W_d$-module structure on the tensor product $Potimes M$. We prove in this paper that any simple $W_d$-module that is finitely generated over the cartan subalgebra is a quotient module of the $W_d$-module $P otimes M$ for a finite dimensional simple $mathfrak{gl}_d$-module $M$ and a simple $mathcal{K}_d$-module $P$ that are finitely generated over the cartan subalgebra. We also characterize all simple $mathcal{K}_d$-modules and all simple admissible $widetilde W_d$-modules that are finitely generated over the cartan subalgebra.
We discuss tilting modules of affine quasi-hereditary algebras. We present an existence theorem of indecomposable tilting modules when the algebra has a large center and use it to deduce a criterion for an exact functor between two affine highest wei
ght categories to give an equivalence. As an application, we prove that the Arakawa-Suzuki functor [Arakawa-Suzuki, J. of Alg. 209 (1998)] gives a fully faithful embedding of a block of the deformed BGG category of $mathfrak{gl}_{m}$ into the module category of a suitable completion of degenerate affine Hecke algebra of $GL_{n}$.
We identify level one global Weyl modules for toroidal Lie algebras with certain twists of modules constructed by Moody-Eswara Rao-Yokonuma via vertex operators for type ADE and by Iohara-Saito-Wakimoto and Eswara Rao for general type. The twist is g
iven by an action of $mathrm{SL}_{2}(mathbb{Z})$ on the toroidal Lie algebra. As a byproduct, we obtain a formula for the character of the level one local Weyl module over the toroidal Lie algebra and that for the graded character of the level one graded local Weyl module over an affine analog of the current Lie algebra.
We construct a family of homomorphisms between Weyl modules for affine Lie algebras in characteristic p, which supports our conjecture on the strong linkage principle in this context. We also exhibit a large class of reducible Weyl modules beyond level one, for p not necessarily small.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
