An estimate of canonical dimension of groups based on Schubert calculus
Rostislav Devyatov
TL;DR
This paper explores the relationship between the canonical dimension of semisimple split simply connected groups and the cohomology of their flag varieties, providing new estimates for exceptional groups of type E.
Contribution
It establishes a novel connection between canonical dimension and flag variety cohomology, leading to improved estimates for exceptional groups.
Findings
New estimate of canonical dimension for exceptional groups of type E
Connection between group canonical dimension and flag variety cohomology
Sketch of proof linking these mathematical concepts
Abstract
We sketch the proof of a connection between the canonical (0-)dimension of semisimple split simply connected groups and cohomology of their full flag varieties. Using this connection, we get a new estimate of the canonical (0-)dimension of simply connected split exceptional groups of type understood as a group.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology