Memoirs of the American Mathematical Society

2 total works

Spectra of Symmetrized Shuffling Operators

by Victor Reiner, Franco Saliola, and Volkmar Welker

Published 1 March 2014

For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of ""O -noninversions"" of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.

Cell Complexes, Poset Topology and the Representation Theory of Algebras Arising in Algebraic Combinatorics and Discrete Geometry

by Stuart Margolis, Franco Saliola, and Benjamin Steinberg

Published 1 May 2022