# Is there an analogue of the Hive model for Littlewood-Richardson coefficients of types $B$, $C$ and $D$?

If $V_\lambda$, $V_\mu$ and $V_\nu$ are irreducible representations of $GL_n$, the Littlewood-Richardson coefficient $c_{\lambda\mu}^\nu$ denotes the multiplicity of $V_\nu$ in the direct sum decomposition of the tensor product of $V_\lambda$ and $V_\nu$. Knutson and Tao proposed a Hive model" for Littlewood-Richardson coefficients in http://www.ams.org/journals/jams/1999-12-04/S0894-0347-99-00299-4/S0894-0347-99-00299-4.pdf

Is there an analogous model for such tensor product multiplicities for Lie groups of types B, C or D?

-

There are conjectural ones in the Berenstein-Zelevinsky paper referenced in that one. They have another paper with a general theorem, Tensor product multiplicities, canonical bases and totally positive varieties, that gives (many) polyhedral models for any Lie type.

-
Hi Allen, Thank you very much. I think I heard that there may be a model for type B, where 3 hives are pasted together to form a Moebius strip, but otherwise the model is similar to the hive model for type A. I'd be very grateful if you could clarify if this is the case. –  Hari Jul 30 '10 at 22:49