Weight space
From Encyclopedia of Mathematics
A finite-dimensional space 
carrying a representation 
of a Lie algebra 
over a field 
and satisfying the following condition: there exists a function 
such that for any 
, 
,
 |
for some positive integer 
. The function 
is called the weight. The tensor product 
of two representations 
of 
with weight spaces 
which have weights 
and 
, respectively, is the representation of 
in the space 
, which is also a weight space and has the weight 
. On passing from the representation 
to the contragredient representation 
, the space 
is replaced by the adjoint space 
, and 
is replaced by 
.
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How to Cite This Entry:
Weight space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weight_space&oldid=49195
Weight space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Weight_space&oldid=49195
This article was adapted from an original article by E.N. Kuz'min (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article