A recent paper of Bump, McNamara and Nakasuji introduced a factorial version of Tokuyama’s identity, expressing the partition function of six vertex model as the product of a t-deformed Vandermonde and a Schur function. Here we provide an extension of their result by exploiting the language of primed shifted tableaux, with its proof based on the use of non-interesecting lattice paths.

We prove that the Banach algebra formed by the space of compact operators on a Hilbert space endowed with the Schur product is a quotient of a uniform algebra (also known as a Q-algebra). Together with a similar result of PérezGarćıa for the trace class, this completes the answer to a long-standing question of Varopoulos.

An old theorem of Sylvester states that a product of k consecutive positive integers each exceeding k is divisible by a prime greater than k. We shall give a proof of this theorem and apply it to prove a result of Schur on the irreducibility of certain polynomials.

We propose a hyperbolic counterpart of the Schur decomposition, with the emphasis on the preservation of structures related to some given hyperbolic scalar product. We give results regarding the existence of such a decomposition and research the properties of its block triangular factor for various structured matrices.

We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of GL(n, C) is isomorphic to another. As a consequence we discover families of LittlewoodRichardson coefficients that are non-zero, and a condition on Schur non-negativity.

We describe a generalization of Hashimoto and Kurano's Cauchy filtration for divided powers algebras. This is then used to provide cellular structure generalized Schur algebras associated an arbitrary algebra. Applications the cellularity wreath product A ? S d are also considered.

Abstract In this paper, we investigate some properties of ideals in group algebras finite groups over fields. First, highlight an important link between their dimension, minimal Hamming distance and the order. This is a generalized version uncertainty principle shown 1992 by Meshulam. Secondly, introduce notion Schur product module structure dimension square. We give structural result on that c...

A complete system of primitive pairwise orthogonal idempotents for cyclotomic Hecke algebras is constructed by consecutive evaluations of a rational function in several variables on quantum contents of multi-tableaux. This function is a product of two terms, one of which depends only on the shape of the multi-tableau and is proportional to the inverse of the corresponding Schur element.