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We classify the simple bounded weight modules of ${mathfrak{sl}(infty})$, ${mathfrak{o}(infty)}$ and ${mathfrak{sp}(infty)}$, and compute their annihilators in $U({mathfrak{sl}(infty}))$, $U({mathfrak{o}(infty))}$, $U({mathfrak{sp}(infty))}$, respectively.
We use analogues of Enrights and Arkhipovs functors to determine the quiver and relations for a category of $mathfrak{sl}_2 ltimes L(4)$-modules which are locally finite (and with finite multiplicities) over $mathfrak{sl}_2$. We also outline serious
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
With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $mathfrak{gl}(n)$-module $V$, and the set $S$, we obtain impo
Kostants weight $q$-multiplicity formula is an alternating sum over a finite group known as the Weyl group, whose terms involve the $q$-analog of Kostants partition function. The $q$-analog of the partition function is a polynomial-valued function de
Let $mathfrak{a},mathfrak{b}$ be two ideals of a commutative noetherian ring $R$ and $M$ a finitely generated $R$-module.~We continue to study $textrm{f}textrm{-}mathrm{grad}_R(mathfrak{a},mathfrak{b},M)$ which was introduced in [Bull. Malays. Math.