Kronecker coefficients and noncommutative super Schur functions
نویسندگان
چکیده
منابع مشابه
Skew Quasisymmetric Schur Functions and Noncommutative Schur Functions
Recently a new basis for the Hopf algebra of quasisymmetric functions QSym, called quasisymmetric Schur functions, has been introduced by Haglund, Luoto, Mason, van Willigenburg. In this paper we extend the definition of quasisymmetric Schur functions to introduce skew quasisymmetric Schur functions. These functions include both classical skew Schur functions and quasisymmetric Schur functions ...
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We develop a theory of Schur functions in noncommuting variables, assuming commutation relations that are satissed in many well-known associative algebras. As an application of our theory, we prove Schur-positivity and obtain generalized Littlewood-Richardson and Murnaghan-Nakayama rules for a large class of symmetric functions, including stable Schubert and Grothendieck polynomials.
متن کاملThe stability of the Kronecker product of Schur functions
In the late 1930’s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n large enough, the values of the Kronecker coefficients appearing in the product of two Schur functions of degree n do not depend on the first part of the indexing partitions, but only on the values of their remaining parts. We compute the exact value of n when ...
متن کاملLecture 6 : Kronecker Product of Schur Functions – Part I
The irreducible representations of Sn, i.e. the Specht modules are indexed by partitions λ of n. For any two partitions λ, μ of n, Sλ ⊗ Sμ = gλμνSν , for suitable integers gλμν . The actual values of these coefficients still eludes us. We look at a formula (admittedly messy), which gives the exact values of gλμν for simple shapes λ, μ.
متن کاملKronecker coefficients via Symmetric Functions and Constant Term Identities
This work lies across three areas of investigation that are by themselves of independent interest. A problem that arose in quantum computing led us to a link that tied these areas together. This link led to the calculation of some Kronecker coefficients by computing constant terms and conversely the computations of certain constant terms by computing Kronecker coefficients by symmetric function...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2018
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2018.02.007