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Littlewood–Richardson rule
In
mathematics
, the
Littlewood–Richardson rule
is a combinatorial description of the coefficients that arise when decomposing a product of two
Schur functions
as a linear combination of other Schur functions. These coefficients are natural numbers, which the Littlewood–Richardson rule describes as counting certain
skew tableaux
. They occur in many other mathematical contexts, for instance as
multiplicity
in the decomposition of
tensor products
of
irreducible representations
of
general linear groups
(or related groups like the
special linear
and
special unitary groups
), or in the decomposition of certain
induced representations
in the
representation theory of the symmetric group
, or in the area of
algebraic combinatorics
dealing with
Young tableaux
and
symmetric polynomials
.
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