Highest-weight vectors for the adjoint action of GLnon polynomials

HIGHEST-WEIGHT VECTORS FOR THE ADJOINT ACTION OF GLn ON POLYNOMIALS, II

Generalized Drinfeld Polynomials for Highest Weight Vectors of the Borel Subalgebra of the Sl2 Loop Algebra

In a Borel subalgebra U(B) of the sl2 loop algebra, we introduce a highest weight vector Ψ. We call such a representation of U(B) that is generated by Ψ highest weight. We define a generalization of the Drinfeld polynomial for a finitedimensional highest weight representation of U(B). We show that every finitedimensional highest weight representation of the Borel subalgebra is irreducible if th...

Tau-functions as highest weight vectors for W1+∞ algebra

For each r = (r1, r2, . . . , rN ) ∈ C N we construct a highest weight module Mr of the Lie algebra W1+∞. The highest weight vectors are specific tau-functions of the N -th Gelfand–Dickey hierarchy. We show that these modules are quasifinite and we give a complete description of the reducible ones together with a formula for the singular vectors. hep-th/9510211

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field

Bethe states as highest weight vectors of the sl 2 loop algebra at roots of unity

We show that regular Bethe ansatz eigenvectors of the XXZ spin chain at roots of unityare highest weight vectors and generate irreducible representations of the sl2 loop algebra.Here the parameter q, which is related to the XXZ anisotropy ∆ through ∆ = (q+q−1)/2,is given by a root of unity, q2N = 1, for an integer N . First, for a regular Bethe stateat a root of unity, we sh...