Related papers: Contributions of Issai Schur to Analysis

Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in…

By defining two important terms called basic perturbation vectors and obtaining their linear bounds, we obtain the linear componentwise perturbation bounds for unitary factors and upper triangular factors of the generalized Schur…

Gorsky and Negut introduced operators $Q_{m,n}$ on symmetric functions and conjectured that, in the case where $m$ and $n$ are relatively prime, the expression ${Q}_{m,n}(1)$ is given by the Hikita polynomial ${H}_{m,n}[X;q,t]$. Later,…

We make a broad conjecture about the $k$-Schur positivity of Catalan functions, symmetric functions which generalize the (parabolic) Hall-Littlewood polynomials. We resolve the conjecture with positive combinatorial formulas in cases which…

We discuss orbifold version of the Schur index defined as the supersymmetric partition function in S^3/Z_n x S^1. We first give a general formula for Lagrangian theories obtained by localization technique, and then suggest a generalization…

In 2004 Rosas and Sagan asked whether there was a way to define a basis in the algebra of symmetric functions in noncommuting variables, NCSym, having properties analogous to the classical Schur functions. This was because they had…

Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory [1,2,3,4]. In this letter we briefly expound the relationship found between the restricted Schurs and the…

Inspired by a recent work of M. Nakasuji, O. Phuksuwan and Y. Yamasaki we combine interpolated multiple zeta values and Schur multiple zeta values into one object, which we call interpolated Schur multiple zeta values. Our main result will…

In this article, we will prove the Giambelli formula for Schur multiple zeta-functions of extended shape which we call laced type, using the combinatorial method of proving the Giambelli formula for Schur function by Egecioglu and Remmel.…

Let $E$ be a $W^{\ast}$-correspondence over a von Neumann algebra $M$ and let $H^{\infty}(E)$ be the associated Hardy algebra. If $\sigma$ is a faithful normal representation of $M$ on a Hilbert space $H$, then one may form the dual…

Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…

The main goal of this paper is to reconsider a phenomenon which was treated in earlier work of the authors' on several truncated matricial moment problems. Using a special kind of Schur complement we obtain a more transparent insight into…

We apply a theorem of Geronimus to derive some new formulas connecting Schur functions with orthogonal polynomials on the unit circle. The applications include the description of the associated measures and a short proof of Boyd's result…

Let D be a masa in B(H) where H is a separable Hilbert space. We find real numbers \eta_0 < \eta_1 < \eta_2 < ... < \eta_6 so that for every bounded, normal D-bimodule map {\Phi} on B(H) either ||\Phi|| > \eta_6, or ||\Phi|| = \eta_k for…

We determine the precise conditions under which any skew Schur function is equal to a Schur function over both infinitely and finitely many variables.

We give a presentation of Schur algebras (over the rational number field) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the…

We introduce partially defined Schur multipliers and obtain necessary and sufficient conditions for the existence of extensions to fully defined positive Schur multipliers, in terms of operator systems canonically associated with their…

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be…

We present a formulas to add a row or a column to the power, monomial, forgotten, Schur, homogeneous and elementary symmetric functions. As an application of these operators we show that the operator that adds a column to the Schur…

We consider commuting operators obtained by quantization of Hamiltonians of the Hopf (aka dispersionless KdV) hierarchy. Such operators naturally arise in the setting of Symplectic Field Theory (SFT). A complete set of common eigenvectors…