Computational aspects of the Cohomology of Coxeter arrangements: On Conjectures of Lehrer-Solomon and Felder-Veselov

点击翻译按钮获取中文摘要

Coxeter groups are groups of symmetries which form part of many physical theories about the world we live in. Moreover, these groups are frequently found at the heart of deep mathematical theories, most notably Lie theory. This project is concerned with two seemingly unrelated algebras, the Orlik-Solomon algebra and the Descent algebra, both of which describe certain geometric and combinatorial aspects of the underlying Coxeter group. Experimental evidence suggests the existence of surprising connections between these two algebras. These have been formulated as two precise conjectures about decompositions of certain natural representations of these algebras. A proof, even of special cases of these conjectures, will greatly enhance our understanding of Coxeter groups and the algebras associated to them and potentially impact on other theories involving these groups of symmetries.