Related papers: Irreducibility criterion for the set of two matric…
Given a weakly decreasing positive integer sequence $\lambda = (\lambda_1,\dotsc,\lambda_\ell)$ summing to $n$, let $\chi^\lambda$ denote the irreducible character of the symmetric group $S_n$ indexed by $\lambda$. This representation has…
We study irreducible restrictions from modules over alternating groups to subgroups. We get reduction results which substantially restrict the classes of subgroups and modules for which this is possible. This is known when the…
Let $S$ be a smooth projective surface over $\mathbb{C}$. Let $S^{[n_1,\dots,n_k]}$ denote the nested Hilbert scheme which parametrizes zero-dimensional subschemes $\xi_{n_1} \subset \ldots \subset \xi_{n_k}$ where $\xi_i$ is a closed…
Let $\Lambda$ be a finite dimensional string algebra over a field with the quiver $Q$ such that the underlying graph of $Q$ is a tree, and let $|\Det(\Lambda)|$ be the number of the minimal right determiners of all irreducible morphisms…
Given an nxn nilpotent matrix over an algebraically closed field K, we prove some properties of the set of all the nxn nilpotent matrices over K which commute with it. Then we give a proof of the irreducibility of the variety of all the…
For an element $a$ of an integral domain D under an equivalence relation \tau, the \tau-factorization of a is defined as \lambda a_1 a_2... a_k, where \lambda is a unit in D and a_i \tau a_j for all i, j. An irreducible element has no…
Given a connected semisimple Lie group $G$ and an arithmetic subgroup $\Gamma$, it is well-known that each irreducible representation $\pi$ of $G$ occurs in the discrete spectrum $L^2_{\text{disc}}(\Gamma\backslash G)$ of…
Topical maps are a nonlinear generalization of nonnegative matrices acting on the interior of the standard cone $\mathbb{R}^n_{\ge 0}$. Several analogues of irreducibility have been defined for topical maps, and all are sufficient to…
The irreducible alternative superbimodules are studied. The complete classification is obtained for even bimodules of arbitrary dimension and for finite-dimensional irreducible superbimodules over an algebraically closed field.
We derive bounds on the eigenvalues of a generic form of double saddle-point matrices. The bounds are expressed in terms of extremal eigenvalues and singular values of the associated block matrices. Inertia and algebraic multiplicity of…
Lapid and M\'{i}nguez gave a criterion of the irreducibility of the parabolic induction $\sigma \times \pi$, where $\sigma$ is a ladder representation and $\pi$ is an arbitrary irreducible representation of the general linear group over a…
The infinite upper triangular Pascal matrix is $T = [\binom{j}{i}]$ for $0\leq i,j$. It is easy to see that any leading principle square submatrix is triangular with determinant $1$, hence invertible. In this paper, we investigate the…
The problem of classification of infinite subalgebras of Cend_N and of gc_N that acts irreducibly on $\Bbb C[\partial]^N$ is discussed in this paper.
We give a necessary condition for the existence of a path of n irreducible morphisms between indecomposable modules whose composition lies in the (n + 1)-power of the radical. In order to do that, we consider the general criterion given by…
We present a necessary and sufficient condition for a finite-dimensional highest weight representation of the $sl_2$ loop algebra to be irreducible. In particular, for a highest weight representation with degenerate parameters of the…
In Part 1, we classify (indecomposable) objects in the perfect derived category $\mathrm{per}\Lambda$ of a graded skew-gentle algebra $\Lambda$, generalizing technique/results of Burban-Drozd and Deng to the graded setting. We also use the…
In this paper we show that any irreducible finite dimensional representation of $SL_{n+1}$ remains indecomposable if restricted to n--dimensional abelian subalgebras spanned by simple root vectors.
We prove a criterion for the irreducibility of an integral group representation \rho over the fraction field of a noetherian domain R in terms of suitably defined reductions of \rho at prime ideals of R. As applications, we give…
We give a numerical characterization of mutual orthogonality (that is, complementarity) for subalgebras. In order to give such a characterization for mutually orthogonal subalgebras $A$ and $B$ of the $k \times k$ matrix algebra…
Criterion for a companion matrix to have a certain number of flat portions on the boundary of its numerical range is given. The criterion is specialized to the cases of 3-by-3 and 4-by-4 matrices. In the latter case, it is proved that a…