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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 .
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 -