Hives and the fibres of the convolution morphism

Joel Kamnitzer ^[1]
1. [1] Tsinghua-UC Berkeley Shenzhen Institute
  
  Tsinghua-UC Berkeley Shenzhen Institute
  
  Estados Unidos
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 3, 2007, págs. 483-496
Idioma: inglés
DOI: 10.1007/s00029-007-0044-6
Enlaces
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Resumen
- 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 GLn, 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.