论文标题
划分双图双启发功能的0-Hecke模块
0-Hecke modules for row-strict dual immaculate functions
论文作者
论文摘要
我们介绍了甲合压函数的新基础，即行 - 策略双重完美的函数。我们为这些函数构建了一个环状，不可分解的0-算代数模块。我们的行图无染原函数与Berg-Bergeron-Saliola-Serrano-Zabrocki（2014-15）的双重完美函数有关，该函数属于准对称函数环上的划分$ψ$。我们通过0-Hecke Action对标准ImmaCulate Tableaux引起的POSET进行明确描述$ψ$对相关0-Hecke模块的效果。这种出色的POSET揭示了其他0-Hecke子模块和商模块，通常是环状和不可分解的，特别是对于Assaf-Searles（2019）研究的扩展Schur函数的行类似类似物。 像双重完美的函数一样，行分节式双重完美函数是合适的tableaux集的生成函数，对应于特定的下降集。我们通过为下降集的剩余变化构建0-Hecke模块来提供完整的组合理论图片，并表明\ emph {ash asph {ash asph {ash asph {ash and}生成tableaux函数的可能变化是作为由这些下降集确定的0-Hecke模块的特性而发生的。
We introduce a new basis of quasisymmetric functions, the row-strict dual immaculate functions. We construct a cyclic, indecomposable 0-Hecke algebra module for these functions. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution $ψ$ on the ring of quasisymmetric functions. We give an explicit description of the effect of $ψ$ on the associated 0-Hecke modules, via the poset induced by the 0-Hecke action on standard immaculate tableaux. This remarkable poset reveals other 0-Hecke submodules and quotient modules, often cyclic and indecomposable, notably for a row-strict analogue of the extended Schur functions studied in Assaf-Searles (2019). Like the dual immaculate function, the row-strict dual immaculate function is the generating function of a suitable set of tableaux, corresponding to a specific descent set. We give a complete combinatorial and representation-theoretic picture by constructing 0-Hecke modules for the remaining variations on descent sets, and showing that \emph{all} the possible variations for generating functions of tableaux occur as characteristics of the 0-Hecke modules determined by these descent sets.
