Stability of the Heisenberg Product on Symmetric Functions

2017/01/12 by Li Ying, Ying, Li
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT

paper · pdf · doi:10.48550/arxiv.1701.03203

16 pages

arxiv created 2018/07/17 · arxiv updated 2018/07/19

Abstract

The Heisenberg product is an associative product defined on symmetric functions which interpolates between the usual product and the Kronecker product. In 1938, Murnaghan discovered that the Kronecker product of two Schur functions stabilizes. We prove an analogous result for the Heisenberg product of Schur functions.

Related

• The stability of the Kronecker products of Schur functions
• Generalized Stability of Heisenberg Coefficients
• Stability of coefficients in the Kronecker product of a hook and a rectangle
• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
• The Heisenberg product: from Hopf algebras and species to symmetric functions