2003/11/16 by Patricia Hersh
Mathematics · #math.CO #math.AC #msc:05E25 #msc:06A11 #msc:13A50 #msc:52B40
published as J. Pure and Appl. Alg. 178 (2003), no. 3, 255-272 · With an appendix by Vic Reiner
arxiv created 2003/11/16 · arxiv updated 2009/12/01
We study the quotient complex Δ(Blm)/Sl\wr Sm as a means of deducing facts about the ring k[x1,..., xlm]Sl\wr Sm. It is shown in [He] that this quotient complex is shellable when l=2, implying Cohen-Macaulayness of k[x1,..., x2m]S2\wr Sm for any field k. We now confirm for all pairs (l,m) with l>2 and m>1 that this quotient complex is not Cohen-Macaulay over \integ /2\integ , but it is Cohen-Macaulay over fields of characteristic p>m (independent of l). This yields corresponding characteristic-dependent results for the ring of invariants k[x1,..., xlm]Sl\wr Sm. We also prove that this quotient complex and the links of many of its faces are collapsible, and we give a partitioning for this quotient complex.