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The Hyperbolic Formal Affine Demazure Algebra

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Abstract

In the present paper we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of a formal Demazure lattice in the Kac-Moody setting and show that all the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, ON K1N 6N5, Canada

    Marc-Antoine Leclerc

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  1. Marc-Antoine Leclerc
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Correspondence to Marc-Antoine Leclerc.

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Presented by Michel Brion.

This paper will be part of the author’s PhD thesis written under the supervision of Erhard Neher and Kirill Zainoulline. It was partially supported by the NSERC Discovery grants of the supervisors.

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Leclerc, MA. The Hyperbolic Formal Affine Demazure Algebra. Algebr Represent Theor 19, 1043–1057 (2016). https://doi.org/10.1007/s10468-016-9610-y

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  • DOI: https://doi.org/10.1007/s10468-016-9610-y

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