The hyperbolic formal affine Demazure algebra
Marc-Antoine Leclerc
TL;DR
This paper extends the formal affine Demazure algebra to Kac-Moody settings with extendable weight lattices and establishes an isomorphism between the hyperbolic formal Demazure algebra and the Hecke algebra.
Contribution
It introduces extendable weight lattices in Kac-Moody theory and proves an isomorphism with the Hecke algebra for the hyperbolic formal group law.
Findings
Formal Demazure algebra extends to Kac-Moody lattices.
Isomorphism between hyperbolic formal Demazure algebra and Hecke algebra.
Properties of Demazure operators hold in the extended setting.
Abstract
In the present paper we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malag\'on-L\'opez, Savage and Zainoulline in two directions. First, we introduce and study the notion of an extendable weight 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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