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Showing 1 to 10 of 10 for “"Schur functions"”.
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Supersymmetric Schur functions and Lie superalgebra representations
… representations in terms of supersymmetric S-functions. Although this is certainly true for the covariant and contravariant tensor representations2, where the supersymmetric S-function is labelled by a single partition λ, it is not so for the mixed tensor representations3 where the …
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Comparing products of Schur functions and quasisymmetric functions
… case of Lascoux-Leclerc-Thibon's conjecture on Schur positivity of certain differences of products of Schur functions are proved. In the first part of the work a combinatorial method is developed that allows to prove weaker versions of those conjectures. In the second part a recent result of …
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Combinatorics of permutation patterns, interlacing networks, and Schur functions
… involution gives some interesting identities of Schur functions generalizing identities by Fulmek-Kleber. Then we study the balanced swap graphs, which encode a class of Schur function identities obtained this way.
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Odd symmetric functions and categorification
… in and around the theory of symmetric functions. The most basic of these is the Hopf superalgebra of odd symmetric functions. This algebra is neither (super-)commutative nor (super-)cocommutative, yet its combinatorics still exhibit many of the striking integrality and positivity …
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Specht modules and Schubert varieties for general diagrams
The algebra of symmetric functions, the representation theory of the symmetric group, and the geometry of the Grassmannian are related to each other via Schur functions, Specht modules, and Schubert varieties, all of which are indexed by partitions and their Young diagrams. We will generalize these …
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Several Problems Concerning Multivariate Functions and Associated Operators
… two distinct problems about multivariate functions and their associated operators. It first discusses the structure of Agler decompositions, which give useful ways to represent two-variable Schur functions on the bidisk using positive kernels. An elementary proof of the existence of Agler …
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Fermionic Diagonal Coinvariants
… is a difference of Kronecker product of two hook Schur functions. In addition we consider a module $M_{n,m}$ spanned by $m$-ary strings of length $n$. When $m = 2$, as a vector space, $M_{n,2} \cong \mb{C}[X_n] / \langle x_1^2, \ldots, x_n^2 \rangle$. The trivial component of $\dr_n \otimes …
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Polynomials in algebraic combinatorics
… is to study bases of the rings of symmetric functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous functions, however, the introduction of K-theoretic combinatorics has led to increased interest in finding inhomogeneous deformations of classical bases. …
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Combinatorics of ribbon tableaux
… begins with the study of a class of symmetric functions ... Which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the …
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Studies on quasisymmetric functions
… Ira Gessel introduced the ring of quasisymmetric functions (QSym), an extension of the ring of symmetric functions and nowadays one of the standard examples of a combinatorial Hopf algebra. In this thesis, I elucidate three aspects of its theory: 1) Gessel's P-partition enumerators are …