Document Type
Article
Publication Date
9-2-2014
Publication Title
Communications in Algebra
Abstract
We give an explicit (new) morphism of modules between H∗T (G/P)⊗H∗T (P/B) and H∗T (G/B) and prove (the known result) that the two modules are isomorphic. Our map identifies submodules of the cohomology of the flag variety that are isomorphic to each of H∗T (G/P) and H∗ T (P/B). With this identification, the map is simply the product within the ring H∗T (G/B). We use this map in two ways. First we describe module bases for H∗T (G/B) that are different from traditional Schubert classes and from each other. Second we analyze a W-representation on H∗T (G/B) via restriction to subgroups WP. In particular we show that the character of the Springer representation on H∗T (G/B) is a multiple of the restricted representation of WP on H∗T (P/B).
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Rights
Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.
Recommended Citation
Drellich, Elizabeth and Tymoczko, Julianna, "A Module Isomorphism Between H∗T (G/P)⊗H∗T (P/B) and H∗T (G/B)" (2014). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/37
Comments
Peer reviewed accepted manuscript.
Both authors were partially supported by NSF grant DMS–1248171. The second author was partially supported by an Alfred P. Sloan Research Fellowship.