Related papers: The Pieri Rule at Infinity

In an attempt to get some information on the multiplicative structure of the Green ring we study algebraic modules for simple groups, and associated groups such as quasisimple and almost-simple groups. We prove that, for almost all groups…

Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…

If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a…

Let g be a complex finite-dimensional simple Lie algebra. Given a positive integer k and a dominant weight \lambda, we define a preorder on the set $P(\lambda, k)$ of k-tuples of dominant weights which add up to \lambda. Let $P(\lambda,…

In this paper we study extensions between finite-dimensional simple modules over classical Lie superalgebras $\mathfrak{gl}(m|n), \mathfrak{osp}(M|2n)$ and $\mathfrak{q}_m$. We consider a simplified version of the extension graph which is…

Let $R$ be a ring essentially of finite type over an $F$-finite field. Given an ideal $\mathfrak{a}$ and a principal Cartier module $M$ we introduce the notion of a $V$-filtration of $M$ along $\mathfrak{a}$. If $M$ is $F$-regular then this…

In this paper we discuss the structure of the tensor product V'_{\alpha,\beta}\otimes L(c,h) of irreducible module from intermediate series and irreducible highest weight module over the Virasoro algebra. We generalize Zhang's…

Let $kE$ denote the group algebra of an elementary abelian $p$-group of rank $r$ over an algebraically closed field of characteristic $p$. We investigate the functors $\mathcal{F}_i$ from $kE$-modules of constant Jordan type to vector…

In this paper, we investigate the irreducible tensor product modules over the planar Galilean conformal algebra $\mathcal{G}$ named by Aizawa, which is the infinite-dimensional Galilean conformal algebra introduced by Bagchi-Gopakumar in…

Let $\mathfrak{g}$ be a symmetrizable Kac-Moody Lie algebra and let $\rho$ denote the sum of the fundamental weights. The irreducible highest weight representations $V(m\rho)$ occupy a distinguished position in representation theory due to…

Let $P$ be a principal indecomposable module of a finite group $G$ in characteristic $2$ and let $\varphi$ be the Brauer character of the corresponding simple $G$-module. We show that $P$ affords a non-degenerate $G$-invariant quadratic…

We prove a noncommutative Bader-Shalom factor theorem for lattices with dense projections in product groups. As an application of this result and our previous works, we obtain a noncommutative Margulis factor theorem for all irreducible…

Let $M$ be a free module of rank $m$ over a commutative unital ring $R$ and let $N$ be its free submodule. We consider the problem when a given element of the exterior product $\Lambda^pM$ is divisible, in a sense, over elements of the…

In this paper, we first obtain a general result on sufficient conditions for tensor product modules to be simple over an arbitrary Lie algebra. We classify simple modules with a nice property over the infinite-dimensional Heisenberg algebra…

Let L be a finite-dimensional semisimple Lie algebra with a non-degenerate invariant bilinear form, \sigma an elliptic automorphism of L leaving the form invariant, and A a \sigma-invariant reductive subalgebra of L, such that the…

Let $F$ be an arbitrary field and let $f:V\times V\to F$ be a non-degenerate symmetric or alternating bilinear form defined on an $F$-vector space of finite dimension $m\geq 2$. Let $L(f)$ be the subalgebra of $gl(V)$ formed by all…

Let G be a semi simple linear algebraic group over a field of characteristic zero and let V be a finite dimensional irreducible G-module with highest weight vector v. Let P in G be the parabolic subgroup fixing v and let g=Lie(G). We get a…

We use tilting modules to study the structure of the tensor product of two simple modules for the algebraic group $\SL_2$, in positive characteristic, obtaining a twisted tensor product theorem for its indecomposable direct summands.…

We study induced modules of nonzero central charge with arbitrary multiplicities over affine Lie algebras. For a given pseudo parabolic subalgebra ${\mathcal P}$ of an affine Lie algebra ${\mathfrak G}$, our main result establishes the…

We obtain several rigidity results regarding tensor product decompositions of factors. First, we show that any full factor with separable predual has at most countably many tensor product decompositions up to stable unitary conjugacy. We…