Quivers play an important role in the representation theory of algebras, with a key ingredient being the path algebra and the preprojective algebra. Quiver grassmannians are varieties of submodules of a fixed module of the path or preprojective algebra. In the current paper, we study these objects in detail. We show that the quiver grassmannians corresponding to submodules of certain injective ...

We first present a filtration on the ring Ln of Laurent polynomials such that direct sum decomposition its associated graded grLn agrees with grLn, as module over complex general linear Lie algebra gl(n), into simple submodules. Next, generalizing modules occurring in we give some explicit constructions weight multiplicity-free irreducible representations gl(n).

In this paper, we study Weyl modules for a toroidal Lie algebra \(\mathcal {T}\) with arbitrary n variables. Using the work of Rao (Pac. J. Math. 171(2), 511–528 1995), prove that level one global are isomorphic to suitable submodules Fock space representation up twist. As an application, compute graded character local module {T}\), thereby generalising Kodera (Lett. Phys. 110(11) 3053–3080 202...

let $m_r$ be a module with $s=end(m_r)$. we call a submodule $k$ of $m_r$ annihilator-small if $k+t=m$, $t$ a submodule of $m_r$, implies that $ell_s(t)=0$, where $ell_s$ indicates the left annihilator of $t$ over $s$. the sum $a_r(m)$ of all such submodules of $m_r$ contains the jacobson radical $rad(m)$ and the left singular submodule $z_s(m)$. if $m_r$ is cyclic, then $a_r(m)$ is the unique ...

We study the coinvariant ring of the complex reflection group G(r, p, n) as a module for the corresponding rational Cherednik algebra H and its generalized graded affine Hecke subalgebra H. We construct a basis consisting of non-symmetric Jack polynomials, and using this basis decompose the coinvariant ring into irreducible modules for H. The basis consists of certain non-symmetric Jack polynom...

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

We study the coinvariant ring of the complex reflection group G(r, p, n) as a module for the corresponding rational Cherednik algebra H and its generalized graded affine Hecke subalgebra H. We construct a basis consisting of non-symmetric Jack polynomials, and using this basis decompose the coinvariant ring into irreducible modules forH. The basis consists of certain non-symmetric Jack polynomi...

We introduce the notion of E-depth graded modules over polynomial rings to measure depth certain Ext modules. First, we characterize with (sufficiently) large as those whose partial general initial submodules preserve Hilbert function local cohomology supported at irrelevant maximal ideal, extending a result Herzog and Sbarra on sequentially Cohen-Macaulay Second, describe cone tables sufficien...