We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges-Rovnyak space H(KS) as the state space for the unique (up to unitary equivalence) observable, coisometric transfer-function realization of the Schur-class multiplier S, realization-theoretic characterization of inner Schur-class mult...

We consider the problem of embedding the semi-ring of Schur-positive symmetric polynomials into its analogue for the classical types B/C/D. If we preserve highest weights and add the additional Lie-theoretic parity assumption that the weights in images of Schur functions lie in a single translate of the root lattice, there are exactly two solutions. These naturally extend the Kirillov–Reshetikh...

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

This paper is devoted to deformation theory of "anabelian" representations of the absolute Galois group landing in outer automorphism group of the algebraic fundamental group of a hyperbolic smooth curve defined over a number-field. In the first part of this paper, we obtained several universal deformations for Lie-algebra versions of the above representation using the Schlessinger criteria for...

Any Schur ring is uniquely determined by a partition of the elements group. In this paper we present general technique for enumerating rings over cyclic groups using traditional rings. We also survey recent efforts to enumerate specific orders.

We make use of the representation theory of the innnite dimensional Lie algebras a 1 , b 1 and b sl 2 to derive explicit formulas relating Schur's P-functions to Schur's S-functions. R esum e Nous utilisons la th eorie des repr esentations des alg ebres de Lie de dimension innnie a 1 , b 1 et b sl 2 pour obtenir des formules explicites reliant les fonctions P de Schur aux fonctions S de Schur.

In this article, we describe the Schur multiplier and representation group of discrete Heisenberg groups their t-variants. We give a construction all complex finite-dimensional irreducible projective representations these groups.