In a first part, we are concerned with the relationships between polynomials in the two generators of the algebra of Heisenberg—Weyl, its Bargmann—Fock representation with differential operators and the associated one-parameter group.Upon this basis, the paper is then devoted to the groups of Riordan matrices associated to the related transformations of matrices (i.e., substitutions with prefunctions). Thereby, various properties are studied arising in Riordan arrays, in the Riordan group and, more specifically, in the "striped" Riordan subgroups; further, a striped quasigroup and a semigroup are also examined. A few applications to combinatorial structures are also briefly addressed in the Appendix.
@article{10_37236_5264,
author = {Silvia Goodenough and Christian Lavault},
title = {Overview on {Heisenberg-Weyl} algebra and subsets of {Riordan} subgroups},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5264},
zbl = {1323.05134},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5264/}
}
TY - JOUR
AU - Silvia Goodenough
AU - Christian Lavault
TI - Overview on Heisenberg-Weyl algebra and subsets of Riordan subgroups
JO - The electronic journal of combinatorics
PY - 2015
VL - 22
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5264/
DO - 10.37236/5264
ID - 10_37236_5264
ER -
%0 Journal Article
%A Silvia Goodenough
%A Christian Lavault
%T Overview on Heisenberg-Weyl algebra and subsets of Riordan subgroups
%J The electronic journal of combinatorics
%D 2015
%V 22
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5264/
%R 10.37236/5264
%F 10_37236_5264
Silvia Goodenough; Christian Lavault. Overview on Heisenberg-Weyl algebra and subsets of Riordan subgroups. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5264
