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Polynomial Total Positivity and High Relative Accuracy Through Schur Polynomials
In this paper, Schur polynomials are used to provide a bidiagonal decomposition of polynomial collocation matrices. The symmetry of Schur polynomials...
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Schur–Weyl dualities for the rook monoid: an approach via Schur algebras
The rook monoid, also known as the symmetric inverse monoid, is the archetypal structure when it comes to extend the principle of symmetry. In this...
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Schur Functions
As a warmup for our discussion of Macdonald polynomials, we review fundamental properties of Schur functions. We start here with two definitions of...
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Combinatorial Formula for Schur Polynomials
In the previous chapter we made the following observation: in all our examples the coefficients of Schur polynomials were nonnegative integers. As we...
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Littlewood-Richardson rule for generalized Schur Q-functions
Littlewood-Richardson rule gives the expansion formula for decomposing a product of two Schur functions as a linear sum of Schur functions, while the...
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On the Carathéodory–Schur interpolation problem over quaternions
We consider the quaternion version of the Toeplitz matrix extension problem with prescribed number of negative eigenvalues. The positive semidefinite...
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Schur Polynomials
Along with symmetric polynomials we can consider skew-symmetric polynomials. Let us find out some things about them.
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Schur Q-Polynomials and Kontsevich–Witten Tau Function
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich–Witten tau function as a linear expansion of Schur...
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Demazure crystals and the Schur positivity of Catalan functions
Catalan functions, the graded Euler characteristics of certain vector bundles on the flag variety, are a rich class of symmetric functions which...
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The Schur–Sato Theory for Quasi-elliptic Rings
AbstractThe notion of quasi-elliptic rings appeared as a result of an attempt to classify a wide class of commutative rings of operators arising in...
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GOOD FILTRATIONS FOR GENERALIZED SCHUR ALGEBRAS
Given a quasi-hereditary superalgebra A , the first author and R. Muth have defined generalized Schur bi-superalgebras T A ( n ) and proved that these...
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Symplectic and supersymmetric schur Q-functions, universal characters and integrable hierarchies
Symplectic Schur Q-functions are a symplectic analogue of Schur Q-functions and defined by combinatorial methods. In this paper, we will show that...
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POLYNOMIAL FUNCTORS AND TWO-PARAMETER QUANTUM SYMMETRIC PAIRS
We develop a theory of two-parameter quantum polynomial functors. Similar to how (strict) polynomial functors give a new interpretation of polynomial...
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On axially rational regular functions and Schur analysis in the Clifford-Appell setting
In this paper we start the study of Schur analysis for Cauchy–Fueter regular quaternionic-valued functions, i.e. null solutions of the Cauchy–Fueter...
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Implicitisation and Parameterisation in Polynomial Functors
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations....
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Some remarks on Schur multiplicator of a group being torsion-free
Let G be a group. Among many other results, it is well known that the Schur multiplicator of G (the second integral homology group of G ) is...
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Sharpening Bounds for Multilinear Schur Multipliers
In this paper we make a brief survey of major estimates for norms and traces of multilinear Schur multipliers. We also discuss several open problems...
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The positive Schur property on positive projective tensor products and spaces of regular multilinear operators
We characterize the positive Schur property in the positive projective tensor products of Banach lattices, we establish the connection with the weak...
