## 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

**-equivariant cohomology of Grassmannians.***GL(N)*Original language | English |
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Pages (from-to) | 169-214 |

Number of pages | 45 |

Journal | Journal of Combinatorial Algebra |

Volume | 2 |

Issue number | 2 |

Early online date | 8 May 2018 |

DOIs | |

Publication status | Published - 2018 |