New mathematical framework tackles operators in abstract algebra
Researchers have developed a new approach to Demazure operators applied to double cosets, extending tools used in automorphic forms and modular function theory. The work builds on recent advances in differential operators and could streamline computational methods in number theory and related fields that depend on these mathematical structures.
Originaltitel: Demazure operators for double cosets
<p>For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category we call the nilCoxeter category, and we also present this category by generators and relations. We prove a generalization to this context of Demazure's celebrated theorem on Frobenius extensions. This generalized theorem serves as a criterion for ensuring the proper behavior of singular Soergel bimodules. </p>