Springer fibers and Schubert points |
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Institution: | 1. Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO 63130, United States;2. Department of Mathematics, Smith College, Northampton, MA 01063, United States |
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Abstract: | Springer fibers are subvarieties of the flag variety parametrized by partitions; they are central objects of study in geometric representation theory. Schubert varieties are subvarieties of the flag variety that induce a well-known basis for the cohomology of the flag variety. This paper relates these two varieties combinatorially. We prove that the Betti numbers of the Springer fiber associated to a partition with at most three rows or two columns are equal to the Betti numbers of a specific union of Schubert varieties. |
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