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Preprint
Kronecker coefficients for one hook shape
arXiv (Cornell University)
10 Sep 2012
Abstract
We give a positive combinatorial formula for the Kronecker coefficient
g_{lambda mu(d) nu} for any partitions lambda, nu of n and hook shape mu(d) :=
(n-d,1^d). Our main tool is Haiman's \emph{mixed insertion}. This is a
generalization of Schensted insertion to \emph{colored words}, words in the
alphabet of barred letters \bar{1},\bar{2},... and unbarred letters 1,2,... We
define the set of \emph{colored Yamanouchi tableaux of content lambda and total
color d} (CYT_{lambda, d}) to be the set of mixed insertion tableaux of colored
words w with exactly d barred letters and such that w^{blft} is a Yamanouchi
word of content lambda, where w^{blft} is the ordinary word formed from w by
shuffling its barred letters to the left and then removing their bars. We prove
that g_{lambda mu(d) nu} is equal to the number of CYT_{lambda, d} of shape nu
with unbarred southwest corner.
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Details
- Title
- Kronecker coefficients for one hook shape
- Creators
- Jonah Blasiak
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862388104721