in his paper mentioned in the title, which appears in the same issue of this journal, mehdi radjabalipour derives the cyclic decomposition of an algebraic linear transformation. a more general structure theory for linear transformations appears in irving kaplansky's lovely 1954 book on infinite abelian groups. we present a translation of kaplansky's results for abelian groups into the...

We study the explicit formula of Lusztig’s integral forms of the level one quantum affine algebra Uq(ŝl2) in the endomorphism ring of symmetric functions in infinitely many variables tensored with the group algebra of Z. Schur functions are realized as certain orthonormal basis vectors in the vertex representation associated to the standard Heisenberg algebra. In this picture the Littlewood-Ric...

We study a class of algebras associated with linear spaces and its relations with polymatroids and integral posets, i.e. posets supporting homogeneous ASL. We prove that the base ring of a transversal polymatroid is Koszul and describe a new class of integral posets. As a corollary we obtain that every Veronese subring of a polynomial ring is an ASL.

A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any polynomial ring generated by quadratic monomials. The toric ideal of relations between these generators is generated by a set of graphically described binomials. The spectra of the original ring and of its integral closure turn out to be canonicall...

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary symmetric polynomial or a complete homogeneous symmetric polynomial. Thus, we generalize the classical Pieri’s rule for symmetric polynomials/Grassmann varietie...