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We provide a classification and an explicit realization of all irreducible Gelfand-Tsetlin modules of the complex Lie algebra sl(3). The realization of these modules uses regular and derivative Gelfand-Tsetlin tableaux. In particular, we list all simple Gelfand-Tsetlin sl(3)-modules with infinite-dimensional weight spaces. Also, we express all simple Gelfand-Tsetlin sl(3)-modules as subquotionets of localized Gelfand-Tsetlin E_{21}-injective modules.
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
We introduce the notion of essential support of a simple Gelfand-Tsetlin $mathfrak{gl}_n$-module as an important tool towards understanding the character formula of such module. This support detects the weights in the module having maximal possible G
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 a
We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive groups to the
In their study of the equivariant K-theory of the generalized flag varieties $G/P$, where $G$ is a complex semisimple Lie group, and $P$ is a parabolic subgroup of $G$, Lenart and Postnikov introduced a combinatorial tool, called the alcove paths mod