in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

Abstract Let G be a simple complex algebraic group, and let $K \subset G$ reductive subgroup such that the coordinate ring of $G/K$ is multiplicity-free -module. We consider -algebra structure $\mathbb C[G/K]$ study decomposition into irreducible summands product -submodules in . When spherical roots generate root system type $\mathsf A$ , we propose conjectural rule, which relies on conjecture...

Introduction. This paper is meant as an introduction and a guide to some recent developments in real algebraic geometry — more precisely, in semialgebraic geometry. In real algebraic geometry one is concerned with the set of real points V(R) of a variety V defined over R. More generally, one may replace the field of real numbers R by any real closed field. Real algebraic geometry is clearly a p...

Given a finite set E and a family F={E1,. . . ,Em} of subsets of E such that F covers E, the famous unicost set covering problem (USCP) is to determine the smallest possible subset of F that also covers E. We study in this paper a variant, called the Large Set Covering Problem (LSCP), which differs from the USCP in that E and the subsets Ei are not given in extension because they are very large...

On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and covariance conditions. We call \emph{quantum operations} $\mathcal{A}$ the subset extreme such maps. The usual automorphisms (the invertible *-algebra morphisms) are examples quantum operations, we show ...

in this paper we will give the character table of the irreducible rational representations of g=sl (2, q) where q= , p prime, n>o, by using the character table and the schur indices of sl(2,q).

‎in this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎then we discuss the existence of o-basis‎ ‎of these classes‎.

Let j : Y → X be a continuous surjection of compact metric spaces. Whyburn proved that is irreducible , meaning ( F ) ⊊ for any proper closed subset if and only almost one-to-one in the sense { y ∈ card − 1 = } ‾ . In this note we prove following generalization: There exists unique minimal set K ⊆ such x Translated to language operator algebras, says A B unital inclusion separable abelian C ⁎ -...

Although describing very different physical systems, both the Klein–Gordon equation for tachyons (m2<0) and Helmholtz share a remarkable property: unitary irreducible representation of corresponding invariance group on suitable subspace solutions is only achieved if non-local scalar product defined. Then, subset oscillatory supports unirrep Euclidean group, with m2<0 tachyonic Poincaré gr...