So, 〈(A ∗B)ei, ej〉 = 〈Aei, ej〉 〈Bei, ej〉 . The Schur product theorem states that if A,B ∈ L (C) are positive then their Hadamard product A ∗B is positive. 1John B. Conway, A Course in Functional Analysis, second ed., p. 33, Proposition 2.12. 2John B. Conway, A Course in Functional Analysis, second ed., p. 34, Proposition 2.13. 3Ward Cheney and Will Light, A Course in Approximation Theory, p. 81...

Let Hn,r be the Ariki-Koike algebra associated to the complex reflection group Sn (Z/rZ)n, and let S(Λ) be the cyclotomic q-Schur algebra associated to Hn,r, introduced by Dipper, James and Mathas. For each p = (r1, . . . , rg) ∈ Zg>0 such that r1 + · · · + rg = r, we define a subalgebra Sp of S(Λ) and its quotient algebra S. It is shown that Sp is a standardly based algebra and S is a cellular...

We investigate a family of MϕA-h-convex functions, give some properties it and several inequalities which are counterparts to the classical such as Jensen inequality Schur inequality. weighted Hermite-Hadamard for an function estimations product two functions.

The Iwahori-Hecke algebra Hk(q ) of type A acts on tensor product space V ⊗k of the natural representation of the quantum superalgebra Uq(gl(m, n)). We show this action of Hk(q ) and the action of Uq(gl(m, n)) on the same space determine commuting actions of each other. Together with this result and Gyoja’s q-analogue of the Young symmetrizer, we construct a highest weight vector of each irredu...

In this paper we present a comparison of the service disciplines in real-time queueing systems (the customers have a deadline before which they should enter the service booth). We state that the more a service discipline gives priority to customers having an early deadline, the least the average stationary lateness is. We show this result by comparing adequate random vectors with the Schur-Conv...

In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.

We apply ideas from crystal theory to affine Schubert calculus and flag Gromov–Witten invariants. By defining operators on certain decompositions of elements in the type-A affine Weyl group, we produce a crystal reflecting the internal structure of Specht modules associated to permutation diagrams. We show how this crystal framework can be applied to study the product of a Schur function with a...

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-intersecting lattice paths.

We show that certain tensor product multiplicities in semisimple braided sovereign tensor categories must be even. The quantity governing this behavior is the Frobenius--Schur indicator. The result applies in particular to the representation categories of large classes of groups, Lie algebras, Hopf algebras and vertex algebras.