We use Kazhdan-Lusztig tensoring to, first, describe annihilating ideals of highest weight modules over an affine Lie algebra in terms of the corresponding VOA and, second, to classify tilting functors, an affine analogue of projective functors known in the case of a simple Lie algebra.

For an untwisted affine Kac-Moody Lie algebra g̃, and a given positive integer level k, vertex operators x(z) = ∑ x(n)z−n−1, x ∈ g, generate a vertex operator algebra V . For the maximal root θ and a root vector xθ of the corresponding finite-dimensional g, the field xθ(z) k+1 generates all annihilating fields of level k standard g̃-modules. In this paper we study the kernel of the normal order p...

This paper deals with the formation control of a group of point masses subject to ideal Coulomb friction. We propose a discontinuous controller which provides a solution to the exact formation problem in the presence of ideal Coulomb friction.

Spectral properties of special matrices matrices have been widely applied. We focus on monomial matrices over a finite field Fp, p 6= 2. We describe a way to find the minimal annihilating polynomial, a set of linearly independent eigenvectors.

Pairs (A,B) of mutually annihilating operators AB = BA = 0 on a finite dimensional vector space over an algebraically closed field were classified by Gelfand and Ponomarev [Russian Math. Surveys 23 (1968) 1–58] by method of linear relations. The classification of (A,B) over any field was derived by Nazarova, Roiter, Sergeichuk, and Bondarenko [J. Soviet Math. 3 (1975) 636–654] from the classifi...