An equivariant basis for the cohomology of Springer fibers
| Autor: | Martha Precup, Edward Richmond |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Computer Science::Machine Learning
Pure mathematics Computer Science::Digital Libraries 01 natural sciences Mathematics::Algebraic Topology Cohomology ring Statistics::Machine Learning Mathematics - Algebraic Geometry Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics Equivariant cohomology Mathematics - Combinatorics 0101 mathematics Mathematics::Representation Theory Algebraic Geometry (math.AG) Mathematics Flag (linear algebra) 010102 general mathematics General Medicine Monomial basis Cohomology Computer Science::Mathematical Software Equivariant map 010307 mathematical physics Combinatorics (math.CO) Variety (universal algebra) Quotient ring |
| Popis: | Springer fibers are subvarieties of the flag variety that play an important role in combinatorics and geometric representation theory. In this paper, we analyze the equivariant cohomology of Springer fibers for $GL_n(\mathbb{C})$ using results of Kumar and Procesi that describe this equivariant cohomology as a quotient ring. We define a basis for the equivariant cohomology of a Springer fiber, generalizing a monomial basis of the ordinary cohomology defined by De Concini and Procesi and studied by Garsia and Procesi. Our construction yields a combinatorial framework with which to study the equivariant and ordinary cohomology rings of Springer fibers. As an application, we identify an explicit collection of (equivariant) Schubert classes whose images in the (equivariant) cohomology ring of a given Springer fiber form a basis. 30 pages, 2 figures. Minor revisions |
| Databáze: | OpenAIRE |
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