Related papers: Classification of skew multiplicity free modules

The reducible Specht modules for the Hecke algebra $\mathcal{H}_{\mathbb{F},q}(\mathfrak{S}_n)$ have been classified except when $q=-1$. We prove one half of a conjecture which we believe classifies the reducible Specht modules when $q=-1$…

Let $\mathbb{K}$ denote an algebraically closed field and $A$ a free product of finitely many semisimple associative $\mathbb{K}$-algebras. We associate to $A$ a finite acyclic quiver $\Gamma$ and show that the category of finite…

Let G be a connected reductive linear algebraic group over a field k of characteristic p>0. Let p be large enough with respect to the root system. We show that if a finitely generated commutative k-algebra A with G-action has good…

We study group action on bimodules and bimodule categories and prove for them analogues of the results known for representations of skew group algebras, mainly in the case, when the action is separable.

A group is said to be cube-free if its order is not divisible by the cube of any prime. Let $f_{cf,sol}(n)$ denote the isomorphism classes of solvable cube-free groups of order $n$. We find asymptotic bounds for $f_{cf,sol}(n)$ in this…

In the first part of the paper we give the denominator identity for all simple finite-dimensional Lie super algebras $\frak g\/$ with a non-degenerate invariant bilinear form. We give also a character and (super) dimension formulas for all…

Let ${\bf G}$ be a connected reductive algebraic group defined over the finite field $\mathbb{F}_q$ with $q$ elements,where $q$ is a power of a prime number $p$. Let $\Bbbk$ be a field and we study the extensions of certain $\bk\bg$-modules…

Suppose that $Q$ is a finite quiver and $G\subseteq \Aut(Q)$ is a finite group, $k$ is an algebraic closed field whose characteristic does not divide the order of $G$. For any algebra $\Lambda=kQ/{\mathcal {I}}$, $\mathcal {I}$ is an…

Let V be a simple vertex operator algebra and G a finite automorphism group. Then there is a natural right G-action on the set of all inequivalent irreducible V-modules. Let S be a finite set of inequivalent irreducible V-modules which is…

Let $G/B$ be a flag variety over $\mathbb C$, where $G$ is a simple algebraic group with a simply laced Dynkin diagram, and $B$ is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. We exhibit slices of the representation theory of $\Lambda$ that are always classifiable in stringent geometric terms. Namely, we prove that, for any…

Let $G$ be a finite group, and let cs$(G)$ be the set of conjugacy class sizes of $G$. Recalling that an element $g$ of $G$ is called a \emph{vanishing element} if there exists an irreducible character of $G$ taking the value $0$ on $g$, we…

Let M, N be free modules over a Noetherian commutative ring R and let F be a field such that card(F) does not exceed the continuum. Then : (1) The assertion that [Any two F-vector spaces with isomorphic duals are isomorphic] is equivallent…

Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak k\subset\mathfrak g$ be a reductive in $\mathfrak g$ subalgebra. A $(\mathfrak g, \mathfrak k)$-module is a $\mathfrak g$-module which after restriction to $\mathfrak k$ becomes a…

A semibrick is a set of modules satisfying Schur's Lemma, and it is said to be maximal if it is not properly contained in another semibrick. For any finite dimensional algebra $\varLambda$ over an algebracally closed field $K$, we prove…

A graph is called claw-free if it contains no induced subgraph isomorphic to the complete bipartite graph $K_{1, 3}$. The undirected power graph of a group $G$ has vertices the elements of $G$, with an edge between $g_1$ and $g_2$ if one of…

For a nondegenerate additive subgroup $G$ of the $n$-dimensional vector space $F^n$ over an algebraically closed field $F$ of characteristic zero, there is an associative algebra and a Lie algebra of Weyl type $W(G,n)$ spanned by all…

Let $\mathbb{F}$ be a non-archimedean local field of positive characteristic different from 2. We consider distributions on $\mathrm{GL}(n+1,\mathbb{F})$ which are invariant under the adjoint action of $\mathrm{GL}(n,\mathbb{F})$. We prove…

Let $k$ be a perfect field of prime characteristic $p$, $G$ a finite group scheme over $k$, and $V$ a finite-dimensional $G$-module. Let $S=\mathop{\mathrm{Sym}}V$ be the symmetric algebra with the standard grading. Let $M$ be a $\Bbb…

Let E be an arbitrary directed graph with no restrictions on the number of vertices and edges and let K be any field. We give necessary and sufficient conditions for the Leavitt path algebra L_K(E) to be of countable irreducible…