A DG-extension of symmetric functions arising from higher representation theory

Ilknur Egilmez, Matthew Hogancamp, Aaron D. Lauda, Andrea Appel

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate analogs of symmetric functions arising from an extension of the nilHecke algebra defined by Naisse and Vaz. These extended symmetric functions form a subalgebra of the polynomial ring tensored with an exterior algebra. We define families of bases for this algebra and show that it admits a family of differentials making it a sub-DG-algebra of the extended nilHecke algebra. The ring of extended symmetric functions equipped with this differential is quasi-isomorphic to the cohomology of a Grassmannian. We also introduce new deformed differentials on the extended nilHecke algebra that when restricted makes extended symmetric functions quasi-isomorphic to GL(N)-equivariant cohomology of Grassmannians.
Original languageEnglish
Pages (from-to)169-214
Number of pages45
JournalJournal of Combinatorial Algebra
Volume2
Issue number2
Early online date8 May 2018
DOIs
Publication statusPublished - 2018

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