The power of symmetric functions in noncommutative variables
نویسندگان
چکیده
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. Joint work with E. Briand and M. Rosas
منابع مشابه
Differential Operator Specializations of Noncommutative Symmetric Functions
Let K be any unital commutative Q-algebra and z = (z1, · · · , zn) commutative or noncommutative free variables. Let t be a formal parameter which commutes with z and elements of K. We denote uniformly by K〈〈z〉〉 and K[[t]]〈〈z〉〉 the formal power series algebras of z over K and K[[t]], respectively. For any α ≥ 1, let D〈〈z〉〉 be the unital algebra generated by the differential operators of K〈〈z〉〉 ...
متن کاملGrothendieck Bialgebras, Partition Lattices, and Symmetric Functions in Noncommutative Variables
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra.
متن کاملNoncommutative Symmetric Functions and the Inversion Problem
Abstract. Let K be any unital commutative Q-algebra and z = (z1, z2, · · · , zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [Z6], for each automorphism Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a NCS (noncommutative symmetric) system ([Z5]) ΩFt has been constructed. Cons...
متن کاملThe primitives of the Hopf algebra of noncommutative symmetric functions
Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theore...
متن کاملNoncommutative Symmtric Functions and the Inversion Problem
Abstract. Let K be any unital commutative Q-algebra and z = (z1, z2, · · · , zn) commutative or noncommutative variables. Let t be a formal central parameter and K[[t]]〈〈z〉〉 the formal power series algebra of z over K[[t]]. In [Z6], for each automorphism Ft(z) = z−Ht(z) of K[[t]]〈〈z〉〉 with Ht=0(z) = 0 and o(H(z)) ≥ 1, a NCS (noncommutative symmetric) system ([Z5]) ΩFt has been constructed. Cons...
متن کاملNoncommutative Symmetric Functions VII: Free Quasi-Symmetric Functions Revisited
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〉. ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011