Plethysm for wreath products and homology of sub-posets of Dowling lattices

分划代数与plethysm系数II：分歧plethysm

The partition algebra and the plethysm coefficients II: ramified plethysm

本文利用对称群圈积与分歧分划代数的Schur--Weyl对偶，将plethysm系数解释为模限制的合成因子重数，揭示其首部分较大时的稳定现象，给出μ为单部分时的首个正公式及两类系数的显式公式与组合解释。

Representations of wreath products on cohomology of De Concini-Procesi compactifications

The wreath product W(r,n) of the cyclic group of order r and the symmetric group S_n acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula for the characters of the representations of W(r,n) on the cohomology groups of this compactification, extending the result of Ginzburg and Kapranov in the r=1 case. As a corollary, we get a formula for the Betti numbers which generalizes the result of Yuzvinsky in the r=2 case. Our method involves applying to the nested-set stratification a generalization of…