Weil Representation of a Generalized Linear Group over a Ring of Truncated Polynomials over a Finite Field Endowed with a Second Class Involution

We construct a complex linear Weil representation $\rho$ of the generalized special linear group $G={\rm SL}_*^{1}(2,A_n)$ ($A_n=K[x]/\langle x^n\rangle$, $K$ the quadratic extension of the finite field $k$ of $q$ elements, $q$ odd), where $A_n$ is endowed with a second class involution. After the construction of a specific data, the representation is defined on the generators of a Bruhat presentation of $G$, via linear operators satisfying the relations of the presentation. The structure of a unitary group $U$ associated to $G$ is described. Using this group we obtain a first decomposition of $\rho$

Classification of finite dimensional uniserial representations of conformal Galilei algebras

With the aid of the $6j$-symbol, we classify all uniserial modules of $\mathfrak{sl}(2)\ltimes \mathfrak{h}_{n}$, where $\mathfrak{h}_{n}$ is the Heisenberg Lie algebra of dimension $2n+1$.Comment: Some references added, introduction expanded, title change

Free 2-step nilpotent Lie algebras and indecomposable representations

Given an algebraically closed field F of characteristic 0 and an F-vector space V, let L(V) = V⊕Λ2(V) denote the free 2-step nilpotent Lie algebra associated to V. In this paper, we classify all uniserial representations of the solvable Lie algebra &= ⟨x⟩⋉L(V), where x acts on V via an arbitrary invertible Jordan block.Fil: Cagliero, Leandro Roberto. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaFil: Frez, Luis Gutiérrez. Universidad Austral de Chile; ChileFil: Szechtman, Fernando. University Of Regina; Canad