Title: Quasisymmetric functions, descent sets, immaculate tableaux, and 0-Hecke modulesSpeaker: Shelia Sundaram Affiliation: Location: MC 5479 or contact Olya Mandelshtam for Zoom link
The first half of this talk will be expository and devoted to a discussion of (quasi)symmetric functions and tableaux.
We define new families of quasisymmetric functions, in particular the new basis of row-strict dual immaculate functions, with an associated cyclic, indecomposable 0-Hecke algebra module. Our row-strict immaculate functions are related to the dual immaculate functions of Berg-Bergeron-Saliola-Serrano-Zabrocki (2014-15) by the involution \psi on the ring Qsym of quasisymmetric functions. We uncover the remarkable properties of the immaculate Hecke poset induced by the 0-Hecke action on standard immaculate tableaux, revealing other submodules and quotient modules, often cyclic and indecomposable.