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Results tagged with rt.representation-theory
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user 57843
Linear representations of algebras and groups, Lie theory, associative algebras, multilinear algebra.
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What are the general zonal spherical functions for ${\rm SO}(n)/{\rm SO}(n-1)$?
The zonal spherical functions [1] on the sphere $(G={\rm SO}(n)$, $K={\rm SO}(n-1))$ are the Gegenbauer or ultraspherical polynomials if one considers the irreducible representations of ${\rm SO}(n)$ …
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Is the projector to irreducible tensor modules of SO(N) known?
To project a generic tensor to an irreducible module of SO(N) one has to (anti)symmetrize the indices and then subtract traces, e.g. for symmetric traceless 2-tensors
$$
\frac{1}{2} (\delta_{I_1 J_1} …