Cohomology of a flag variety as a Bethe algebra
R.Rimanyi, V.Schechtman, V.Tarasov, A.Varchenko
TL;DR
This paper establishes a novel connection between the equivariant cohomology of flag varieties and Bethe algebras, providing a new algebraic perspective on geometric structures.
Contribution
It introduces a new interpretation of the equivariant cohomology of flag varieties as Bethe algebras associated with gl_N[t] modules.
Findings
Identifies the equivariant cohomology with Bethe algebra structures
Provides algebraic tools for studying flag varieties
Bridges geometric and algebraic representation theories
Abstract
We interpret the GL_n equivariant cohomology of a partial flag variety of flags of length N in \C^n as the Bethe algebra of a suitable gl_N[t] module associated with the tensor power (\C^N)^{\otimes n}.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Algebraic Geometry and Number Theory