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arXiv · 1709.05212

Macdonald's formula for Kac-Moody groups over local fields

Nicole Bardy-Panse·Stéphane Gaussent·Guy Rousseau
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Abstract

For an almost split Kac-Moody group G over a local non-archimedean field, the last two authors constructed a spherical Hecke algebra H (over the complex numbers C, say) and its Satake isomorphism with the commutative algebra of Weyl invariant elements in some formal series algebra C[[Y]].In this article, we prove a Macdonald's formula, i.e. an explicit formula for the image of a basis element of H. The proof involves geometric arguments in the masure associated to G and algebraic tools, including the Cherednik's representation of the Bernstein-Lusztig-Hecke algebra (introduced in a previous article) and the Cherednik's identity between some symmetrizers.

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BibTeXRIS

Nicole Bardy-Panse, Stéphane Gaussent, Guy Rousseau. 2017-09-15. Macdonald's formula for Kac-Moody groups over local fields. https://doi.org/10.1112/plms.12231

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