The honeycomb model of tensor products I: Proof of the saturation conjecture
Authors:
Allen Knutson and Terence Tao
Journal:
J. Amer. Math. Soc. 12 (1999), 10551090
MSC (1991):
Primary 05E15, 22E46; Secondary 15A42
Published electronically:
April 13, 1999
Part II:
J. Amer. Math. Soc. (2004), 1948
MathSciNet review:
1671451
Fulltext PDF Free Access
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Abstract: Recently Klyachko has given linear inequalities on triples of dominant weights of necessary for the corresponding LittlewoodRichardson coefficient to be positive. We show that these conditions are also sufficient, which was known as the saturation conjecture. In particular this proves Horn's conjecture from 1962, giving a recursive system of inequalities. Our principal tool is a new model of the BerensteinZelevinsky cone for computing LittlewoodRichardson coefficients, the honeycomb model. The saturation conjecture is a corollary of our main result, which is the existence of a particularly wellbehaved honeycomb associated to regular triples .
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Additional Information
Allen Knutson
Affiliation:
Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254
Address at time of publication:
Department of Mathematics, University of California Berkeley, Berkeley, California 947203840
Email:
allenk@alumni.caltech.edu
Terence Tao
Affiliation:
Department of Mathematics, University of California Los Angeles, Los Angeles, California 900951555
Email:
tao@math.ucla.edu
DOI:
http://dx.doi.org/10.1090/S0894034799002994
PII:
S 08940347(99)002994
Keywords:
Honeycombs,
LittlewoodRichardson coefficients,
BerensteinZelevinsky patterns,
Horn's conjecture,
saturation,
Klyachko inequalities
Received by editor(s):
July 31, 1998
Received by editor(s) in revised form:
February 25, 1999
Published electronically:
April 13, 1999
Additional Notes:
The first author was supported by an NSF Postdoctoral Fellowship.
The second author was partially supported by NSF grant DMS9706764.
Article copyright:
© Copyright 1999
American Mathematical Society
