Related papers: A connection between Schur and Dieudonn\'e's theor…
Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. Based on the theory of operator spaces and completely bounded mappings we present norm optimal versions of these…
We analyse the strong connections between spaces of vector-valued Lipschitz functions and spaces of linear continuous operators. We apply these links to study duality, Schur properties and norm attainment in the former class of spaces as…
In this paper we study the low rank matrix completion problem using tools from Schur complement. We give a sufficient and necessary condition such that the completed matrix is globally unique with given data. We assume the observed entries…
We present an extension of the duality theorem, previously defined by S. Catani et al. on the one-loop level, to higher loop orders. The duality theorem provides a relation between loop integrals and tree-level phase-space integrals. Here,…
Grothendieck's inequalities for operators and bilinear forms imply some factorization results for complex m x n matrices. The theory of operator spaces provides a set up which describes 4 norm optimal factorizations of Grothendieck's sort.…
We study Le Potier's strange duality conjecture on a rational surface. We focus on the case involving the moduli space of rank 2 sheaves with trivial first Chern class and second Chern class 2, and the moduli space of 1-dimensional sheaves…
We study Le Potier's strange duality conjecture on a rational surface. We focus on the strange duality map $SD_{c_n^r,L}$ which involves the moduli space of rank $r$ sheaves with trivial first Chern class and second Chern class $n$, and the…
We observe that the Dieudonn\'{e} determinant induces a non-negative degree function on the ring of matrices over a skew polynomial ring. We then apply this degree function to two examples. In the first one, we find an expression for the…
A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…
The use of master actions to prove duality at quantum level becomes cumbersome if one of the dual fields interacts nonlinearly with other fields. This is the case of the theory considered here consisting of U(1) scalar fields coupled to a…
In this paper, we study the Fenchel-Rockafellar duality and the Lagrange duality in the general frame work of vector spaces without topological structures. We utilize the geometric approach, inspired from its successful application by B. S.…
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on…
The main purpose of this paper is to show that the multiplication of a Schubert polynomial of finite type $A$ by a Schur function, which we refer to as Schubert vs. Schur problem, can be understood from the multiplication in the space of…
We show that three notions of rank for matrices of multilinear forms are equivalent. This result generalizes a classical result of Flanders, corrects a minor hole in work of Fortin and Reutenauer, answers a question of Lampert on the…
We use a unified elementary approach to prove the second part of classical, mixed, super, and mixed super Schur-Weyl dualities for general linear groups and supergroups over an infinite ground field of arbitrary characteristic. These…
Applying a general categorical construction for the extension of dualities, we present a new proof of the Fedorchuk duality between the category of compact Hausdorff spaces with their quasi-open mappings and the category of complete normal…
We prove two dichotomy theorems about sequences of operators into $L_1$ given by random matrices. In the second theorem we assume that the entries of each random matrix form a sequence of independent, symmetric random variables. Then the…
The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…
We study the Schur index, the Zhu's $C_2$ algebra, and the Macdonald index of a four dimensional $\mathcal{N}=2$ Argyres-Douglas (AD) theories from the structure of the associated two dimensional $W$-algebra. The Schur index is derived from…
We study duality transformation and duality symmetry in the the electromagnetic-like charged p-form theories. It is shown that the dichotomic characterization of duality groups as $Z_2$ or SO(2) remains as the only possibilities but are now…