Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

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?

share|improve this question

1 Answer 1

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.

share|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.