We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, and , in terms of the first terms in the Taylor towers of and for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of and . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for and .
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-3-1, author = {Brenda Johnson and Randy McCarthy}, title = {Taylor towers of symmetric and exterior powers}, journal = {Fundamenta Mathematicae}, volume = {201}, year = {2008}, pages = {197-216}, zbl = {1182.55010}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-3-1} }
Brenda Johnson; Randy McCarthy. Taylor towers of symmetric and exterior powers. Fundamenta Mathematicae, Tome 201 (2008) pp. 197-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm201-3-1/