The stability of the Kronecker product of Schur functions

被引：33

作者：

Briand, Emmanuel ^{[2
]}

Orellana, Rosa ^{[3
]}

Rosas, Mercedes ^{[1
]}

机构：

[1] Univ Seville, Dept Algebra, E-41012 Seville, Spain

[2] Univ Seville, Dept Matemat Aplicada, E-41012 Seville, Spain

[3] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

来源：

JOURNAL OF ALGEBRA | 2011年 / 331卷 / 01期

关键词：

Kronecker product; Internal product; Symmetric functions; IRREDUCIBLE REPRESENTATIONS; SYMMETRICAL GROUP; CHARACTERS; COEFFICIENTS; PLETHYSMS;

D O I：

10.1016/j.jalgebra.2010.12.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the late 1930s Murnaghan discovered the existence of a stabilization phenomenon for the Kronecker product of Schur functions. For n sufficiently large, 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 for which all the coefficients of a Kronecker product of Schur functions stabilize. We also compute two new bounds for the stabilization of a sequence of coefficients and show that they improve existing bounds of M. Brion and E. Vallejo. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：11 / 27

页数：17

共 26 条

[1]

[Anonymous], CAMBRIDGE STUD ADV M

[2]

Ballantine CM, 2005, ELECTRON J COMB, V12

[3]

BRIAND E, DISCRETE MATH THEORE

[4] Reduced Kronecker Coefficients and Counter-Examples to Mulmuley's Strong Saturation Conjecture SH [J].

Briand, Emmanuel ;

Orellana, Rosa ;

Rosas, Mercedes .

COMPUTATIONAL COMPLEXITY, 2009, 18 (04) :577-600

[5] STABLE PROPERTIES OF PLETHYSM - ON 2 CONJECTURES OF FOULKES [J].

BRION, M .

MANUSCRIPTA MATHEMATICA, 1993, 80 (04) :347-371

[6] SYMMETRIC GROUP - CHARACTERS, PRODUCTS AND PLETHYSMS [J].

BUTLER, PH ;

KING, RC .

JOURNAL OF MATHEMATICAL PHYSICS, 1973, 14 (09) :1176-1183

[7] Nonzero Kronecker coefficients and what they tell us about spectra [J].

Christandl, Matthias ;

Harrow, Aram W. ;

Mitchison, Graeme .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 270 (03) :575-585

[8]

CLAUSEN M, 1993, BAYREUTHER MATH SCHR, V45, P1

[9] ON THE KRONECKER PRODUCT OF S(N) CHARACTERS [J].

DVIR, Y .

JOURNAL OF ALGEBRA, 1993, 154 (01) :125-140

[10] Eigenvalues, invariant factors, highest weights, and Schubert calculus [J].

Fulton, W .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 37 (03) :209-249

← 1 2 3 →