Abstract In this paper, we generalize Schur–Weyl duality and Morita Theorem on associative algebras to those H -pseudoalgebras. Meanwhile, get a plenty of -pseudoalgebras over cocommutative Hopf algebra

The problem of the Robust Stability of Schur Polynomials is investigated. Recently, a new approach based on Rouche's theorem of the classical complex analysis has been adopted for the solution of this problem. In this paper, an improvement of this solution is presented. This is the optimum solution of the Robust Stability problem of Schur Polynomials and is obtained by solving a minimization pr...

We exhibit a “method” for bijective proofs for determinant identities, which is based on translating determinants to Schur functions by the Jacobi–Trudi identity. We illustrate this “method” by generalizing a bijective construction (which was first used by Goulden) to a class of Schur function identities, from which we shall obtain bijective proofs for Dodgson’s condensation formula, Plücker re...

Schur studied limits of the arithmetic means sn of zeros for polynomials of degree n with integer coefficients and simple zeros in the closed unit disk. If the leading coefficients are bounded, Schur proved that lim supn→∞ |sn| ≤ 1− √ e/2. We show that sn → 0, and estimate the rate of convergence by generalizing the Erdős-Turán theorem on the distribution of zeros. To cite this article: I. E. P...

Mason and Ng have given a generalization to semisimple quasiHopf algebras of Linchenko and Montgomery’s generalization to semisimple Hopf algebras of the classical Frobenius-Schur theorem for group representations. We give a simplified proof, in particular a somewhat conceptual derivation of the appropriate form of the Frobenius-Schur indicator that indicates if and in which of two possible fas...