Non‐commutative manifolds, the free square root and symmetric functions in two non‐commuting variables
نویسندگان
چکیده
منابع مشابه
Symmetric Functions in Noncommuting Variables
Consider the algebra Q〈〈x1, x2, . . .〉〉 of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x1, x2, . . .) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In p...
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Let Πn denote the set of all set partitions of {1, 2, . . . , n}. We consider two subsets of Πn, one connected to rook theory and one associated with symmetric functions in noncommuting variables. Let En ⊆ Πn be the subset of all partitions corresponding to an extendable rook (placement) on the upper-triangular board, Tn−1. Given π ∈ Πm and σ ∈ Πn, define their slash product to be π|σ = π∪(σ+m)...
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This article is essentially an appendix to [4]. We gather here some useful properties of the algebra FQSym of free quasi-symmetric functions which were overlooked in [4]. Recall that FQSym is a subalgebra of the algebra of noncommutative polynomials in infinitely many variables ai which is mapped onto Gessel’s algebra of quasi-symmetric functions QSym by the commutative image ai 7→ xi of K〈A〉. ...
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We show that the Kronecker coefficients indexed by two two-row shapes are given by quadratic quasipolynomial formulas whose domains are the maximal cells of a fan. Simple calculations provide explicitly the quasipolynomial formulas and a description of the associated fan. As an application, we characterize all the Kronecker coefficients indexed by two two-row shapes that are equal to zero. Join...
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ژورنال
عنوان ژورنال: Transactions of the London Mathematical Society
سال: 2018
ISSN: 2052-4986,2052-4986
DOI: 10.1112/tlm3.12015