Tensor product varieties and crystals: 𝐺𝐿 case

Malkin, Anton

doi:10.1090/S0002-9947-01-02899-9

Tensor product varieties and crystals: $GL$ case
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Trans. Amer. Math. Soc. 354 (2002), 675-704 Request permission

Abstract:

A geometric theory of tensor product for $\mathfrak {gl}_{N}$-crystals is described. In particular, the role of Spaltenstein varieties in the tensor product is explained, and thus a direct (non-combinatorial) proof of the fact that the number of irreducible components of a Spaltenstein variety is equal to a Littlewood-Richardson coefficient (i.e. certain tensor product multiplicity) is obtained.

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