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Results tagged with rt.representation-theory
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user 40349
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
10
votes
1
answer
517
views
Cauchy identity in three sets of variables?
The Cauchy identity states that
$$
\prod_{i,j} \frac{1}{1-x_i y_j} = \sum_\lambda s_\lambda(x) s_\lambda(y),
$$
where $s_\lambda(x)$ is the Schur function.
Is there a known decomposition of the produ …
- 11.2k
1
vote
Representation Theory of $U(N)$
Regarding (2): In the context of rational complex representations of $GL_n$ vs those of $SL_n$, your extra factor is accounted for by the determinant. Given a rational representation of $GL_n$, $V$, i …
- 273