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arXiv · 2009.00042

Bases of tensor products and geometric Satake correspondence

Pierre Baumann·Stéphane Gaussent·Peter Littelmann
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Abstract

The geometric Satake correspondence can be regarded as a geometric construction of the rational representations of a complex connected reductive group G. In their study of this correspondence, Mirkovi\'c and Vilonen introduced algebraic cycles that provide a linear basis in each irreducible representation. Generalizing this construction, Goncharov and Shen define a linear basis in each tensor product of irreducible representations. We investigate these bases and show that they share many properties with the dual canonical bases of Lusztig.

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Pierre Baumann, Stéphane Gaussent, Peter Littelmann. 2020-08-31. Bases of tensor products and geometric Satake correspondence. https://arxiv.org/abs/2009.00042

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