Document Type

Article

Publication Date

9-2-2014

Publication Title

Communications in Algebra

Abstract

We give an explicit (new) morphism of modules between HT (G/P)⊗HT (P/B) and HT (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 HT (G/P) and H T (P/B). With this identification, the map is simply the product within the ring HT (G/B). We use this map in two ways. First we describe module bases for HT (G/B) that are different from traditional Schubert classes and from each other. Second we analyze a W-representation on HT (G/B) via restriction to subgroups WP. In particular we show that the character of the Springer representation on HT (G/B) is a multiple of the restricted representation of WP on HT (P/B).

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

Rights

Licensed to Smith College and distributed CC-BY under the Smith College Faculty Open Access Policy.

Comments

Both authors were partially supported by NSF grant DMS–1248171. The second author was partially supported by an Alfred P. Sloan Research Fellowship.

Included in

Mathematics Commons

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