Geodesic
Proof of Stembridge's conjecture on stability of Kronecker coefficients
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 1-10.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove a conjecture of Stembridge concerning stability of Kronecker coefficients that vastly generalizes Murnaghan's theorem. The main idea is to identify the sequences of Kronecker coefficients in question with Hilbert functions of modules over finitely generated algebras. The proof only uses Schur-Weyl duality and the Borel-Weil theorem and does not rely on any existing work on Kronecker coefficients.
Classification : 05E10
Keywords: Kronecker coefficients, symmetric group, Hilbert function, Schur-Weyl duality, plethysm, Littlewood-Richardson coefficients, twisted commutative algebras 
@article{JAC_2016__43_1_a11,
     author = {Sam, Steven V. and Snowden, Andrew},
     title = {Proof of {Stembridge's} conjecture on stability of {Kronecker} coefficients},
     journal = {Journal of Algebraic Combinatorics},
     pages = {1--10},
     publisher = {mathdoc},
     volume = {43},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a11/}
}
TY  - JOUR
AU  - Sam, Steven V.
AU  - Snowden, Andrew
TI  - Proof of Stembridge's conjecture on stability of Kronecker coefficients
JO  - Journal of Algebraic Combinatorics
PY  - 2016
SP  - 1
EP  - 10
VL  - 43
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a11/
LA  - en
ID  - JAC_2016__43_1_a11
ER  - 
%0 Journal Article
%A Sam, Steven V.
%A Snowden, Andrew
%T Proof of Stembridge's conjecture on stability of Kronecker coefficients
%J Journal of Algebraic Combinatorics
%D 2016
%P 1-10
%V 43
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a11/
%G en
%F JAC_2016__43_1_a11
Sam, Steven V.; Snowden, Andrew. Proof of Stembridge's conjecture on stability of Kronecker coefficients. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 1-10. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a11/