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Multiplicity relation between highest weight modules, Demazure modules, and crystals
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Similarly, we have that the crystal $B(\nu)$ appears in the tensor product of crystals $B(\lambda) \otimes B(\mu)$ with multiplicity
$$
c_{\lambda, \mu}^\nu:=|\{b \in B(\mu): wt(b)=\nu-\lambda,\ … For the case of highest weight modules and highest weight crystals, I might expect to see a justification of $m_{\lambda, \mu}^\nu = c_{\lambda, \mu}^\nu$ along the lines of a "classical limit" statement …