Results 31 to 40 of about 1,099,967 (179)
Symmetric Functions in Noncommuting Variables [PDF]
, 2002 Consider the algebra Q> of formal power series in countably many noncommuting variables over the rationals. The subalgebra Pi(x_1,x_2,...) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the ...
Bruce, E. Sagan, Mercedes H. Rosas
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Noncommutative symmetric functions with matrix parameters [PDF]
Discrete Mathematics & Theoretical Computer Science, 2012 We define new families of noncommutative symmetric functions and quasi-symmetric functions depending on two matrices of parameters, and more generally on parameters associated with paths in a binary tree. Appropriate specializations of both matrices then
Alain Lascoux +2 more
doaj +1 more source
Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type [PDF]
, 2011 We introduce and study natural generalisations of the Hermite and Laguerre polynomials in the ring of symmetric functions as eigenfunctions of infinite-dimensional analogues of partial differential operators of Calogero-Moser-Sutherland (CMS) type.
Desrosiers, Patrick, Hallnäs, Martin
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Truncated homogeneous symmetric functions [PDF]
Linear and Multilinear Algebra, 2020 Extending the elementary and complete homogeneous symmetric functions, we introduce the truncated homogeneous symmetric function $h_ ^{\dd}$ in $(\ref{THSF})$ for any integer partition $ $, and show that the transition matrix from $h_ ^{\dd}$ to the power sum symmetric functions $p_ $ is given by \[M(h^{\dd},p)=M'(p,m)z^{-1}D^{\dd},\] where $D^{\dd}
Houshan Fu, Zhousheng Mei
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Classical symmetric functions in superspace
, 2005 We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables.
E.M. Moens +14 more
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Vertex operators, solvable lattice models and metaplectic Whittaker functions
, 2020 We show that spherical Whittaker functions on an $n$-fold cover of the general linear group arise naturally from the quantum Fock space representation of $U_q(\widehat{\mathfrak{sl}}(n))$ introduced by Kashiwara, Miwa and Stern (KMS).
Brubaker, Ben +3 more
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Rota--Baxter algebras and left weak composition quasi-symmetric functions
, 2016 Motivated by a question of Rota, this paper studies the relationship between Rota--Baxter algebras and symmetric related functions. The starting point is the fact that the space of quasi-symmetric functions is spanned by monomial quasi-symmetric ...
Guo, Li, Yu, Houyi, Zhao, Jianqiang
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Symmetric Functions, Noncommutative Symmetric Functions And Quasisymmetric Functions II
Acta Applicandae Mathematicae, 2003 This is part two of this survey; to appear in Acta. Appl. Math. The first part appeared in Acta Appl. Math 75 (2003), 55-93 and is also 'arXived'.
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A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions
, 2013 We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose
Berg, Chris +4 more
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, 2020 Hypergeometric functions and zonal polynomials are the tools usually addressed in the literature to deal with the expected value of the elementary symmetric functions in non-central Wishart latent roots.
Di Nardo, E.
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