Hives and the fibres of the convolution morphism

Details Hives and the fibres of the convolution morphism Hives and the fibres of the convolution morphism

2007-05-11

arxiv.org/abs/0705.1698v2

Mathematics

Algebraic Geometry

11 pages

Scientific paper

By the geometric Satake correspondence, the number of components of certain fibres of the affine Grassmannian convolution morphism equals the tensor product multiplicity for representations of the Langlands dual group. On the other hand, in the case of GL_n, combinatorial objects called hives also count tensor product multiplicities. The purpose of this paper is to give a simple bijection between hives and the components of these fibres. In particular, we give a description of the individual components. We also describe a conjectural generalization involving the octahedron recurrence.

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