Extended nilHecke algebra and symmetric functions in type B
Representation Theory
2018-03-20 v2
Abstract
We formulate a type B extended nilHecke algebra, following the type A construction of Naisse and Vaz. We describe an action of this algebra on extended polynomials and describe some results on the structure on the extended symmetric polynomials. Finally, following Appel, Egilmez, Hogancamp, and Lauda, we prove a result analogous to a classical theorem of Solomon connecting the extended symmetric polynomial ring to a ring of usual symmetric polynomials and their differentials.
Cite
@article{arxiv.1710.10698,
title = {Extended nilHecke algebra and symmetric functions in type B},
author = {Michael Reeks},
journal= {arXiv preprint arXiv:1710.10698},
year = {2018}
}
Comments
14 pages. Revised version for publication in Journal of Pure and Applied Algebra. Includes a new section on differentials and DG structure