English

Conjectures on the reduced Kronecker coefficients

Representation Theory 2026-02-02 v4 Combinatorics Category Theory

Abstract

We formulate a series of conjectures on the stable tensor product of irreducible representations of symmetric groups, which are closely related to the reduced Kronecker coefficients. These conjectures are certain generalizations of Okounkov's conjecture on the log-concavity of the Littlewood--Richardson coefficients and the Schur log-concavity theorem of Lam--Postnikov--Pylyavskyy. We prove our conjectures in some special cases and discuss some implications of these conjectures.

Keywords

Cite

@article{arxiv.2210.14668,
  title  = {Conjectures on the reduced Kronecker coefficients},
  author = {Tao Gui},
  journal= {arXiv preprint arXiv:2210.14668},
  year   = {2026}
}

Comments

12 pages. The main Conjecture 5.1 is false and we add counterexamples found by professor Mike Zabrocki in the end

R2 v1 2026-06-28T04:33:03.080Z