Year: 2025
Type: article
Abstract: We investigate the Demazure product in a double affine setting. A recent preprint by Muthiah and Puskás gives a conjectural way to define this in terms of the $$q=0$$ q = 0 specialisation of these Hecke algebras. We instead take a different approach generalising work by Felix Schremmer, who gave an equivalent formula for the (single) affine Demazure product in terms of the quantum Bruhat graph. We focus on type $$\widehat{SL}_2$$ SL ^ 2 , where we prove that the quantum Bruhat graph of this type satisfies some nice properties, which allows us to construct a well-defined associative Demazure product for the double affine Weyl semigroup $$W_\mathcal {T}$$ W T (for level greater than one). We give results regarding the Demazure product and Muthiah and Orr’s length function for $$W_\mathcal {T}$$ W T , and we verify that our proposal matches specific examples computed by Muthiah and Puskás using the Kac-Moody affine Hecke algebra.
Source: Mathematische Zeitschrift
Author: Lewis Dean
Institution: University of Glasgow
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4413865941