Taylor towers of symmetric and exterior powers

Brenda Johnson, and Randy McCarthy. "Taylor towers of symmetric and exterior powers." Fundamenta Mathematicae 201.3 (2008): 197-216. <http://eudml.org/doc/282858>.

@article{BrendaJohnson2008,
abstract = {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, $D_\{k\}Spⁿ$ and $D_\{k\}Λⁿ$, in terms of the first terms in the Taylor towers of $Sp^\{t\}$ and $Λ^\{t\}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $Sp^\{t\}$ and $Λ^\{t\}$. We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_\{k\}Spⁿ$ and $D_\{k\}Λⁿ$.},
author = {Brenda Johnson, Randy McCarthy},
journal = {Fundamenta Mathematicae},
keywords = {symmetric and exterior power functors; Taylor tower of a functor},
language = {eng},
number = {3},
pages = {197-216},
title = {Taylor towers of symmetric and exterior powers},
url = {http://eudml.org/doc/282858},
volume = {201},
year = {2008},
}

TY - JOUR
AU - Brenda Johnson
AU - Randy McCarthy
TI - Taylor towers of symmetric and exterior powers
JO - Fundamenta Mathematicae
PY - 2008
VL - 201
IS - 3
SP - 197
EP - 216
AB - 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, $D_{k}Spⁿ$ and $D_{k}Λⁿ$, in terms of the first terms in the Taylor towers of $Sp^{t}$ and $Λ^{t}$ for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of $Sp^{t}$ and $Λ^{t}$. We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for $D_{k}Spⁿ$ and $D_{k}Λⁿ$.
LA - eng
KW - symmetric and exterior power functors; Taylor tower of a functor
UR - http://eudml.org/doc/282858
ER -